For all problems assume that gravity is 10 m/s^2. A football placekicker consist

Question

For all problems assume that gravity is 10 m/s^2. A football placekicker consistently kicks a football with a resultant velocity of 23 m/s at an angle of 43 degree relative to the horizontal. What is the maximum distance from the goal post the kicker can make a field goal? Assume the bottom bar of the goal post is 10 feet (3.05 m) off of the ground. A Cliff Calamity is going to attempt a dive into the surf. This no simple dive, but a cliff dive from the maximum allowable competitive height of 28 m (about 92 feet). Complicating the dive is some rocks in the surf for about 7 m horizontally from the cliff face. Cliff takes off from the cliff with a vertical velocity of 0 m/s and a horizontal velocity of 3.5 m/s. Does cliff clear the rocks? What is Cliff s vertical velocity at the instant of impact? Quincy Quarterback is doing a NFL tryout. He is trying to impress the observers with his magnificent arm. He can generate a maximum resultant velocity of 19 m/s with his arm. Determine the optimum release angle to maximize throwing distance. Assume that the ball is release 2.1 m above the ground, and that the ball hits the ground (it is not caught).

Explanation / Answer

1. y = 3.05 m .....this have to be minimum vertical dispalcement of ball.

initial vertical velocity, v0y = 23 sin43 = 15.7 m/s

a = -10 m/s^2

y = v0y t + a t^2 / 2

3.05 = 15.7t - 10 t^2 /2

5 t^2 - 15.7 + 3.05 = 0   

t = 0.208 s and 2.93 s

for maximum distance, t = 2.93 sec

In horizontal,

v0x = 23 cos43 = 16.82 m/s

a_x = 0

d = v0x t

= 49.3 m

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