Question

the same instant. What was the initial speed of the second object? An object is dropped from a bridge. A second object is thrown downwards 1.00 s later. They both reach the water 20.0 m below at the same instant. What was the initial speed of the second object? 19.6 m/s 21.3 m/s 14.6 m/s 9.90 m/s 4.91 m/s

Answer 1

Answer:

$v_{o}=-14.60m/s$

Explanation:

Kinematics equation for first Object:

$y(t)=y_{o}+v_{o}t-1/2*g*t^{2}$

but:

$v_{o}=0m/s$       The initial velocity is zero

$y_{o}=20m$

it reach the water at in instant, t1, y(t)=0:

$0=y_{o}-1/2*g*t_{1}^{2}$

$t_{1}=\sqrt{2y_{o}/g}=\sqrt{2*20/9.81}=2.02s$

Kinematics equation for the second Object:

The initial velocity is zero

$y(t)=y_{o}+v_{o}t-1/2*g*t^{2}$

but:

$y_{o}=20m$

it reach the water at in instant, t2, y(t)=0. If the second object is thrown 1s later, t2=t1-1=1.02s

$0=y_{o}+v_{o}t_{2}-1/2*g*t_{2}^{2}$

$v_{o}=1/(t_{2})*(1/2*g*t_{2}^{2}-y_{o})=(1/1.02)*(1/2*9.81*1.02^{2}-20)=-14.60m/s$

The velocity is negative, because the object is thrown downwards.