Question

Three small metal balls are thrown at different speeds off the top of a building to hit the ground 25m below. Sphere A is thrown directly downward at 10m/s, while Sphere B is dropped from rest. Sphere C is thrown upwards at 5m/s. Ignore the effects of air resistance.

Calculate the time for each sphere to hit the ground below. Show your work clearly.

1D Kinematics. Accelerated motion.

Practice Problem Three small metal balls are thrown at different at speeds off the top of a building to hit the ground 25m below. Sphere A is thrown directly downward at 10m/s while sphere B is dropped from rest. Sphere C is thrown upwards at 5m/s. Ignore the effects of air resistance Calculate the time for each sphere to hit the ground below. Show your work clearly.

Answer 1

For sphere A

initial speed is Vo = 10 m/s

distance travelled is h = 25 m

accelaration is =g = 9.8 m/s^2

then using

S = (Vo*t)+(0.5*a*t^2)

25 = (10*t)+(0.5*9.8*t^2)

t = 1.46 sec

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For sphere B

initial speed is Vo= 0 m/s

S = (Vo*t)+(0.5*a*t^2)

25 = (0*t)+(0.5*9.8*t^2)

t = 2.25 sec

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For sphere C

t = t1+t2
t1 is the time taken to reach maximum height

t1 = Vo/g = 5/9.8 = 0.51 sec

maximum height reached is Hmax = Vo^2/(2*g) = 5^2/(2*9.8) = 1.28 m

so the ditance travelled before reaching the ground is

S = 1.28+25 = 26.28 m

then

S = (Vo*t)+(0.5*a*t^2)

26.28 = (0*t)+(0.5*9.8*t^2)

t = 2.32 sec