Mechanics Physics Question

Question

If you throw a ball straight up with an initial speed of 55m/s.

A)How long will the ball remain in the air?

B)What speed should u throw the ball so that it stays in the air for 9 seconds

Answer 1

A)

h = -(1/2)g t² + v0 t

h = -4.9 t² + 55 t

h = 0 when

-4.9 t²  + 55 t = 0

(-4.9 t +55) t = 0

t = 0

t = 55/4.9 = 11 s

The first solution is the moment the ball is thrown up

The second solution is the time for the ball going up then falling down to the ground. The ball remains in the air for 11 second

B)

h = -(1/2)g t² + v0 t

Evaluate v0 so that h = 0 at t = 9 s.

0= (-4.9 * 9 + v0) * 9

v0 = 4.9 * 9 = 44.1 m/s

Answer 2

Your working formula is

Vf - Vo =gT

where

Vf = velocity of ball at its peak = 0

Vo = initial velocity of ball = 55 m/sec (given)

g = acceleration due to gravity - 9.8 m/sec^2

T = time for ball to reach its peak

Substituting values,

0 - 55 = (-9.8)T

NOTE the negative sign attached to the acceleration due to gravity. This simply denotes that the ball is slowing down as it is going up.

Solving for T,

T = 55/9.8 = 5.61 sec.

Total flight time =  total time ball is in the air = time ball goes up + time ball goes down

Total flight time = 5.61 +  5.61 = 11.22 sec.

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For a ball to stay in the air for 9 seconds, the time it will take to reach its peak = 4.5 seconds.

Hence, using the formula above,

Vf - Vo = (-9.8)(4.5)

Vo = 44.1 m/s

Answer 3

A) it will have the same impact velocity when it hits the ground since the graph of its motion is a symmetrical parabola so calculate the time it takes to follow and mulitply by 2 to get total airtime

a=v/t

9.8=55/t

t= 5.612244898

total time=5.6*2= 11.2 seconds

B) if it stays up for 9 seconds that means it takes 4.5 seconds to come down since going up and going down is same time due to symmetical motion neglecting air resistance

so calculate impact velocity which will be same as inital velocity due to symmetrical aspect of motion

a=v/t                              a=v/t

9.8=v/4.5                       32=v/4.5

v= 44.1 m/s       or          v= 144 ft/s

hope this helps