JOHN R. GIBSON, Circuit Judge.

Elbert Rankin was convicted of violating 18 U.S.C. § 922(g)(1) (1988), by being a convicted felon in possession of a firearm. On appeal, he argues that there is insufficient evidence to sustain his conviction, that evidence of other wrongful acts was erroneously admitted at his trial, that the district court improperly rejected a jury instruction proffered by him, and that his sentence is unconstitutional. We affirm the judgment of the district court.

On February 3, 1988, two police officers in a marked police car turned a corner and noticed a person walking on the sidewalk. Upon making eye contact, one of the officers recognized Rankin, who quickened his pace. The officers testified that, as Rankin began to run, he brought his hands to the front of his waist, removed a dark object, and let it fall to the ground. After stopping the car, one of the officers chased Rankin. Simultaneously, the other officer ran to the area where the dark object had been dropped, and found a handgun. The officers followed Rankin into a house and arrested him. The officers testified that the arrest took place within sixty seconds of the time that they initially spotted Rankin. A search of Rankin then revealed a small black leather pouch near the front waistband of his underwear. Inside the pouch, officers discovered a match box and 1.08 grams of cocaine. Rankin, a previously convicted felon, was charged with possession of a firearm and was found guilty by a jury.

I.

In reviewing a challenge to the sufficiency of evidence, our task is not to independently determine whether the defendant is guilty; that job is for the jury. We must instead "resolve evidentiary conflicts in favor of the government, and accept as established all reasonable inferences [in favor of the conviction] that may logically be drawn from the evidence." United States v. Newton, 756 F.2d 53, 54 (8th Cir. 1985). After so construing the evidence, we should "reverse only if a reasonable jury could not have found guilt beyond a reasonable doubt." United States v. Davis, 785 F.2d 610, 619 (8th Cir. 1986). Cf. United States v. Glasser, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942). Here, the officers testified that they saw Rankin drop an object to the ground and that one of the officers discovered a .22 caliber revolver after running directly to the spot where he had seen the object fall. Rankin argues that the government presented no direct evidence connecting him to the firearm because no one saw him either holding a gun or throwing one down. He also argues that the officers' story is inherently suspect because the incident occurred at night on a street without any streetlights, the officers did not use a spotlight, Rankin was wearing a bulky "furry" coat that could have distorted his appearance, and all of the events described by the officers could not have occurred in sixty seconds.

We are not persuaded by Rankin's argument. Although the officers did not testify that the gun they found was the dark object taken from Rankin's waistband, they did state both that Rankin dropped a dark object to the ground and that, after immediately running to the spot where the object fell, one of the officers retrieved a dark gun from that location. We are satisfied that this is sufficient direct and circumstantial evidence to support the conviction. This case is unlike United States v. Beverly, 750 F.2d 34 (6th Cir. 1984) (per curiam), upon which Rankin relies, because there was no proof in that case that the defendant had possessed, rather than merely touched, a gun. See id. at 35-36. Moreover, to the extent that Rankin challenges the credibility of witnesses, he raises questions that were entrusted to the jury. Glasser, 315 U.S. at 80, 62 S.Ct. at 469.

II.

We also reject Rankin's argument that Federal Rule of Evidence 404(b) was transgressed when the court admitted evidence that Rankin possessed cocaine. We believe that Rule 404(b) is inapplicable to the evidence of cocaine. Police officers discovered the cocaine in Rankin's waistband as they arrested him immediately after he fled, discarded the gun, and entered the nearby house. Rankin's possession of cocaine is part of the same criminal event as is his possession of the gun. Thus, the cocaine is not evidence of another wrong, because:

We have held that where evidence of other crimes is "so blended or connected with the one[s] on trial . . . that proof of one incidentally involves the other[s]; or explains the circumstances; or tends logically to prove any element of the crime charged," United States v. Derring, 592 F.2d 1003, 1007 (8th Cir. 1979), it is admissible as an integral part of the immediate context of the crime charged. Id.; see also United States v. Turpin, 707 F.2d 332, 336 (8th Cir. 1983). When the other crimes evidence is so integrated, it is not extrinsic and therefore is not governed by Rule 404(b).

United States v. Bass, 794 F.2d 1305, 1312 (8th Cir.), cert. denied sub nom. 479 U.S. 869, 107 S.Ct. 233, 93 L.Ed.2d 159 (1986); see also United States v. Tate, 821 F.2d 1328, 1331-32 (8th Cir. 1987), cert. denied, 484 U.S. 1011, 108 S.Ct. 712, 98 L.Ed.2d 662 (1988); United States v. Simon, 767 F.2d 524, 526-27 (8th Cir.), cert. denied, 474 U.S. 1013, 106 S.Ct. 545, 88 L.Ed.2d 474 (1985). See generally 2 J. Weinstein M. Berger, Weinstein's Evidence ¶ 404[10], at 404-77 to -80 nn. 18-22 (1989); 22 C. Wright K. Graham, Federal Practice and Procedure § 5239, at 440-43 n. 69 (1978 Supp. 1990).

Even if Rule 404(b) is applicable, it does not support Rankin's argument because it only prevents parties from introducing evidence of other wrongs to demonstrate a propensity to commit crimes; it permits that evidence to be introduced to prove motive, among other things. Evidence that Rankin possessed cocaine could establish a motive for possessing a weapon, and that evidence thus could be admitted without violating Rule 404(b). See United States v. Randle, 815 F.2d 505, 508 (8th Cir. 1987) (discussing the connection between drugs and firearms); Simon, 767 F.2d at 527 (same).

III.

Rankin also argues that the court's jury instructions were improper in two respects. First, he contends that the court erred by rejecting a proposed instruction which both told the jury that testimony by law enforcement officers is not inherently more credible than testimony by other persons and alerted them to the possible biases of law enforcement officers. Our inquiry here is limited, because "[a] district court has wide discretion in formulating appropriate jury instructions. A defendant is not entitled to a particularly worded instruction where the instructions given, when viewed as a whole, adequately and correctly cover the substance of the requested instruction." United States v. Ridinger, 805 F.2d 818, 821 (8th Cir. 1986) (quoting United States v. Reda, 765 F.2d 715, 719 (8th Cir. 1985)) (citations omitted in Ridinger). The district court gave two separate instructions concerning how the jury should evaluate the testimony of witnesses. One of the instructions specifically referred to the credibility and accuracy of the identification of Rankin by Officer Kukla, one of the officers who arrested Rankin. We are satisfied that those instructions as a whole are adequate and correct. Accordingly, we conclude that the court did not abuse its discretion by refusing Rankin's proposed instruction.

Second, Rankin argues that the district court should not have instructed the jury on the doctrine of constructive possession. There was evidence that Rankin took a dark object from his waistband, that he dropped it to the ground, and that a gun was found there. In light of these facts, we believe that the district court did not abuse its discretion by instructing the jury on both actual and constructive possession.

IV.

Finally, Rankin argues that his two year sentence of imprisonment is excessive and unconstitutional. Specifically, he argues: (1) that the Sentencing Guidelines are invalid because they were promulgated in violation of the separation of powers established by the United States Constitution; (2) that the Guidelines violate due process; and (3) that the Guidelines impermissibly authorize judges to consider information that has not been proven true beyond a reasonable doubt. None of these arguments is meritorious. The Supreme Court rejected the separation of powers argument in Mistretta v. United States, 488 U.S. 361, 109 S.Ct. 647, 658-75, 102 L.Ed.2d 714 (1989), this court has repeatedly, and squarely, held that the Guidelines do not violate principles of due process, see, e.g., United States v. Blackman, 897 F.2d 309, 318 (8th Cir. 1990); United States v. Luster, 896 F.2d 1122, 1129 n. 6 (8th Cir. 1990); United States v. White, 890 F.2d 1012, 1013 (8th Cir. 1989); United States v. Barnerd, 887 F.2d 841, 841-42 (8th Cir. 1989) (per curiam); United States v. Nunley, 873 F.2d 182, 186 (8th Cir. 1989); United States v. Brittman, 872 F.2d 827, 828 (8th Cir.), cert. denied, ___ U.S. ___, 110 S.Ct. 184, 107 L.Ed.2d 140 (1989), and it is firmly established that sentencing courts are not limited to considering non-hearsay evidence that has been proven beyond a reasonable doubt, see McMillan v. Pennsylvania, 477 U.S. 79, 91-93, 106 S.Ct. 2411, 2418-20, 91 L.Ed.2d 67 (1986); United States v. Tucker, 404 U.S. 443, 446-47, 92 S.Ct. 589, 591, 30 L.Ed.2d 592 (1972); United States v. Papajohn, 701 F.2d 760, 763 (8th Cir. 1983); see also 18 U.S.C. § 3661 (1988).

Finding no error, we affirm the judgment of the district court.