Question

A ball is thrown upward with an initial velocity of $100m{s}^{-1}.$ Draw velocity-time graph for the ball and find from the graph height of the ball after $15s$. Take $g=10m{s}^{-2}.$

• A. $125m$
  
• B. $375m$
  
• C. $500m$
  
• D. $625m$
  

Answer 1

Answer: (B)

$375m$

Initial velocity of the ball $u=100$ $m/s$

Acceleration of the ball $a=-g=-10$ $m/s^2$

Using $v=u+at$

$\therefore$ $v=100-10t$

Thus $v-t$ graph is a straight line intersecting the t axis at $t=10$ s

Also $v{|}_{t=15}=100-10\left(15\right)=-50$ $m/s^2$

Height (displacement) of the ball is equal to the area under the curve during $0<t<15$

$\therefore$ $h=\frac{1}{2}\times 100\times 10-\frac{1}{2}\times (15-10)\times 50=375$ m