A football is thrown with an initial velocity of 54 mph at a

A football is thrown with an initial velocity of 54 mph at an angle of 31 degrees. How many yards down the field does the ball land?

Distance = XXXX yards

Solution

velocity = 54 mph; angle = 31 deg ; g = 32.17 ft/sec^2

vx = 54cos31 = 46.28 mph = 67.87 ft/sec

vy = 54sin31 = 27.81 mph = 40.78 ft/se

when the ball lands: y =0

y = vy*t -(1/2)gt^2

vy = (1/2)gt

t = 2vy/g = 2*40.78/32.17 = 2.54 sec

Horizontal distance : d = vx*t = 67.87*2.54 = 172.06 ft

= 57.35 yards