Answer to Question #96040 in Mechanics | Relativity for sarah

Question

To win the game, a place kicker must kick a
football from a point 28 m (30.6208 yd) from
the goal, and the ball must clear the crossbar,
which is 3.05 m high. When kicked, the ball
leaves the ground with a speed of 18 m/s at
an angle of 49.4◦from the horizontal.The acceleration of gravity is 9.8 m/s2.
By how much vertical distance does the ball
clear the crossbar?
Answer in units of m.

Answer 1

$$y=y_i+v\cos{49.4\degree}t-0.5gt^2$$

$$t=\frac{x}{v\sin{49.4\degree}}=\frac{28}{18\sin{49.4\degree}}=2.049\ s$$

$$y=0+18\cos{49.4\degree}(2.049)-0.5(9.8)(2.049)^2=3.43\ m$$

$$y-h=3.43-3.05=0.38\ m$$