soccer player kicks a ball at an angle of 37 degrees from the horizontal (ground

Question

soccer player kicks a ball at an angle of 37 degrees from the horizontal (ground with an initial speed of 50 ft/s, assuming the ball follows a parabolic path: level) a) what was the initial velocity of the ball in (i,j) vector-notation b) Find the time at which the ball reaches the highest point of its trajectory. c) How high does the ball go? d) What is the horizontal range of the ball and how long is it in the air? e. What is the velocity of the ball as it strikes the ground? Note: g- 32 ft/s 2 (2) A projectile is shot from the edge of a cliff 125m above ground level with an in of 65 m/s at an angle of 37 degrees with the horizontal, as shown. speed (a) Determine the time taken by the projectile to hit point P at ground level. (b) Determine the range X of the projectile as measured from the base of the cliff. strikes the ground. (e) Find the vertical and horizontal component of the velocity just before the projectile 125 (3) (A) A small body ofmass m = 0.2 kg revolves in a circle on a horizontalfictionless surface, attached by a cord 0.2 m long to a pin set in the center. If the body takes 2 seconds to make a full turn (period), find the centripetal force (the force exerted on the body by the cord). (B) The same body above is twirled in a vertical circle of radius 0.2 m. (a) if the speed is v 2 m/s when the cord makes an angle of 30 degrees with the vertical, find the centripetal force (tension) b) Find the critical speed at the top (that is, the speed when the cord becomes slack) c) If the tension at the bottom is 10 N, find the speed at that point.

Explanation / Answer

1) (A) v0 = (50 cos37)i + (50 sin37)j

v0 = 39.9i + 30.1j ft/s

(B) at highest point, vy = 0

vy = v0y + ay t

0 = 30.1 - 32 t

t = 0.94 sec  

(C) vy^2 - v0y^2 = 2 ay y

0^2 - 30.1^2 = 2(32)(H)

H = 14.2 ft

(D) time of flight = 2t = 1.88 s

X = (v0x) t = (39.9)(1.88)

X =75 ft

(E) vx = v0x = 39.9 ft/s

vy = - v0y = - 30.1 ft/s

v = (39.9 ft/s)i + (-30.1 ft/s) j

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