Sam attempts a 42-yard field goal in a football game. For his attempt to be a success, the football needs to pass through the uprights and over the crossbar that is 10 feet above the ground.
Sam kicks the ball from the ground with an initial velocity of 70 feet per second, at an angle of 50° with the horizontal.
Which statement is true of Sam's attempt?
The ball clears the crossbar by nearly 2 feet.
The ball clears the crossbar by nearly 15 feet.
The ball hits the ground short of the crossbar.
The football clears the crossbar by approximately 6 feet.
I would really appreciate even an equation and where which numbers go and I can solve it myself!!
The time it takes to reach the crossbar is given by the horizontal component of motion
42 yds = 126 ft
126 = 70 cos (50°) * t
126 / [ 70 cos (50°) ] = t = 2.8 sec
The height at any time is
h = -16t^2 + 70sin (50°)t + initial height
At t = 2.8 we have
h = -16(2.8)^2 + 70 sin (50°)(2.8) + 0
h = 24.7 ft
The ball clears the crossbar by about 24.7 - 10 = 14.7 ft = 15 ft