chapter 4 physics webassgin question

Question

A placekicker must kick a football from a point 36.0 m (about 40 yards) from the goal, and half the crowd hopes the ball will clear the crossbar, which is 3.05 m high. When kicked, the ball leaves the ground with a speed of 20.0 m/s at an angle of 46.0° to the horizontal.

 

(a) By how much does the ball clear or fall short of clearing or fall short of clearing the crossbar? (Enter a negative answer if it falls short.)

Answer 1

1. compute the initial horizontal and vertical components of the velocity.

V_ix = 20 cos 46^o = 13.89 m/s = constant

V_iy = 20 sin 46^o = 14.39 m/s

 

2. Determine the time of flight (from initial position to the crossbar).

T = D_x/V_x = 36.0m / 13.89 m/s = 2.59 seconds

 

3. Determine the height of the ball at 2.59 seconds.

a = -g = 9.81 m/s²

D_y = V_iyT + 0.5 aT² = 14.39 x 2.59 + 0.5 x 9.81 x (2.59)² = 4.37 m

This height is higher than the crossbar by 4.37 - 3.05 = 1.32 m