A stone is thrown from the top of the building with an initialvelocity of 20.0m/

Question

A stone is thrown from the top of the building with an initialvelocity of 20.0m/s straight upward, at an initail height of 50.0mabove the ground. Determine: a) the time needed for the stone to reach its maxheight. b) the maximum height c) the time needed for the stone to reach the ground d) the velocity and position of the stone at t =5.00s Please show steps on how to answer the problem A stone is thrown from the top of the building with an initialvelocity of 20.0m/s straight upward, at an initail height of 50.0mabove the ground. Determine: a) the time needed for the stone to reach its maxheight. b) the maximum height c) the time needed for the stone to reach the ground d) the velocity and position of the stone at t =5.00s Please show steps on how to answer the problem

Explanation / Answer

dv = adt v = at + v0 v = -gt + 20
dh = vdt h = -0.5g * t2 + 20 * t + s0 h = -0.5g * t2 + 20 * t + 50
a) This occurs when v=0, so: 0=-gt + 20 t = 20/g = 20/9.81 =2.0 [s]
b) substitute t=2.0 [s] in the equation for h: h = - 0.5 * 9.81 * 2.02 + 20 * 2.0 + 50 = 70.39[m]
c) solve h=0:
h = -0.5g * t2 + 20 * t + 50
Solving this using a calculator gives: t= 5.83 [s]
d) Substitute t=5.00 in the equations for v and h: v = -9.81*5.00 + 20 = -29.05 [m/s] h = - 0.5 * 9.81 * 5.002 + 20 * 5.00 + 50 =27.38 [m]

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