Answer to Question #170059 in Mechanics | Relativity for Stephen Ogu

Question #170059

A ball is projected vertically upward with a velocity of 80m/s. Two seconds later a second ball is projected vertically upward with a velocity of 60m/s. At what point above the surface of earth will they meet?


1
Expert's answer
2021-03-10T17:21:30-0500

Let's take the upwards as the positive direction. After t=2 st=2\ s the first ball reached the height y(2)y(2) and its vertical displacement can be written as follows:


y1=y(2)+v(2)t12gt2.y_1=y(2)+v(2)t-\dfrac{1}{2}gt^2.


Let's find the velocity and height of the first ball after t=2 st=2\ s:


v=v0gt=80 ms9.8 ms22 s=60.4 ms,v=v_0-gt=80\ \dfrac{m}{s}-9.8\ \dfrac{m}{s^2}\cdot2\ s=60.4\ \dfrac{m}{s},y(t=2 s)=80 ms2 s129.8 ms2(2 s)2=140.4 m.y(t=2\ s)=80\ \dfrac{m}{s}\cdot2\ s-\dfrac{1}{2}\cdot9.8\ \dfrac{m}{s^2}\cdot(2\ s)^2=140.4\ m.


Then, we can write the vertical displacement of the second ball projected vertically upward two seconds later:


y2=v02t12gt2y_2=v_{02}t-\dfrac{1}{2}gt^2


At the moment when they meet y1=y2y_1=y_2 and we can write:


y(2)+v(2)t12gt2=v02t12gt2.y(2)+v(2)t-\dfrac{1}{2}gt^2=v_{02}t-\dfrac{1}{2}gt^2.


Substituting y(2)y(2) and v(2)v(2) in the previous equation, we get:


140.4+60.4t12gt2=60t12gt2,140.4+60.4t-\dfrac{1}{2}gt^2=60t-\dfrac{1}{2}gt^2,140.4=0.4t140.4=-0.4tt=351 s.t=-351\ s.

The time is negative, which means that two balls never meet at the height above the earth.


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