The punter on a football team tries to kick a football so that itstays in the ai

Question

The punter on a football team tries to kick a football so that itstays in the air for a long "hang time." If the ball is kicked withan initial velocity of 23.2 m/s at anangle of 62.0° above the ground, what is the "hang time"?
1__________ s

A marble is thrown horizontally with a speed of 8 m/s from the top of a building. When it strikes theground, the marble has a velocity that makes an angle 70° with the horizontal.From what height above the ground was the marble thrown?
1__________ m

A car drives straight off the edge of a cliff that is 48 m high. The police at the scene of the accidentobserved that the point of impact is 135 mfrom the base of the cliff. How fast was the car traveling when itwent over the cliff?
1___________ m/s

Explanation / Answer

part a---------- initial vertical velocity of the ball=23.2*sin62 total displacement of the ball=0 let hang time=t g=acceleration due to gravity=9.8 s=u*t+(1/2)*g*t2 0=23.2*sin62*t -(1/2)*9.8*t2 t=4.18 s (ans) part b------------ let when the marble hit the ground it's velocity was v m/s the marble has horizontal velocity of v*cos70 since horizontal accelerationl is 0 horizontal velocity will remainconstant v*cos70=8 v=23.53 vertical acceleration=g=9.8 initial vertical velocity=u=0 final vertical velocity=v=23.53*sin70=22.11 let height of fall=h v2=u2+2*g*h 22.112=0+2*9.8*h h=24.94 m (ans) part c------------ let the car was traveling at a speed of v m/s when it went over thecliff initial vertical speed=0 vertical acceleration=g=9.8 vertical displacement=48 m let time taken to hit the ground =t h=u*t+(1/2)*g*t2 48=0+(1/2)*9.8*t2 t=3.13 s initial horizontal velocity=v m/s horizontal acceleration=0 horizontal displacement=135 s=u*t+(1/2)*a*t2 135=v*3.13+0 v=43.13 m/s

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