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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!!

 May 15, 2020
 #1
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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

 

 

 

cool cool cool

 May 16, 2020

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