The QB launches a pass into the end zone, 60 yards (54.86m) away, where a receiver is waiting to make the catch. Suppose the QB throws the ball at 55mi/h (24.59m/s). At what angle to the horizontal must the ball be launched in order for it to hit the receiver? Neglect air resistance.
I know i need to use the range equation here, so I'm good on that part, what is confusing me is that the problem also states that there will be two answers for the angle, how would i find the second angle?
Thanks so much!
I know i need to use the range equation here, so I'm good on that part, what is confusing me is that the problem also states that there will be two answers for the angle, how would i find the second angle?
Thanks so much!
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setting up the range equation:
R=v0^2 sin(2 theta)/g
g R/v0^2 = sin( 2 theta)
9.8*54.86/24.59^2 = 0.15
2 theta = arc sin 0.15 = 8.8 deg => theta = 4.4 deg
you will get the same result for theta = 90-4.4 = 85.6 deg
if you substitute this into the sin(2 theta) term, you will see that
sin(2*4.4)=sin(2*85.6) = 0.15
R=v0^2 sin(2 theta)/g
g R/v0^2 = sin( 2 theta)
9.8*54.86/24.59^2 = 0.15
2 theta = arc sin 0.15 = 8.8 deg => theta = 4.4 deg
you will get the same result for theta = 90-4.4 = 85.6 deg
if you substitute this into the sin(2 theta) term, you will see that
sin(2*4.4)=sin(2*85.6) = 0.15