ontal, an 2 Main Question Consider the same setup as in the warm-up questions- a

Question

ontal, an 2 Main Question Consider the same setup as in the warm-up questions- a football is kicked with an initial velocity ot 25 o m/s at an angle 15 above the horizontal. Let's analyze the situation by looking at the first half of the motion le the portion of the motion in which the ball is rising. a) When the ball reaches it's maximum height, what is the ball's yvelocity uy? b) Now using r,(o) equation calculate the time it takes the ball to reach it's maximum height. c) Calculate Vnax- the maximum height that the ball reached, using v(e) equation. d) What is the total time the ball spent in the air? (Hint- use symmetry) e) Using the r(t) equation and total time calculate the range of the projectile. 0 Using the u() and t'y(t) equations, determine the ball's velocity (in terms of its unit vector decomposi tion) at 1.0s. g) Determine the magnitude and direction of the ball's velocity at t 1.0s.

Explanation / Answer

(a) since height is maximum

Y velocity=0m/s

(b)initial vertical velocity=25sin(15)=6.47 m/s

Time taken=6.47/9.8=0.66 sec

(c)let maximum height is H

H=6.47^2/(2*9.8)=2.14 m

(d)total time=2*0.66=1.32sec

Part (e)

Range=25cos(15)*1.32=31.9 m

Part (f)

At t=0

Vy=6.47-(9.8*1)=-3.3m/s

Vx=25cos(15)=24.14 m/s

Part g)

V=24.36 m/s

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