Question

A ball is dropped from a ballon going up at a speed of $4m{s}^{-1}$. If the balloon was at the height of 105 m from the ground at the time of dropping the ball, how long will the ball take to reach the ground? Take (g = 10 ${\mathrm{ms}}^{-2}$)

• A. 5 s
• B. 4.2 s
• C. 6 s
• D. 8.4 s

Answer 1

The correct option is A 5 s

Initial speed, u = 4 m$s^{-1}$ , height S = 105 m , g = 10 m $s^{-2}$ Balloon is moving upwards. So taking into consideration the sign conventions, u = - 4 m $s^{-1}$
Using equation of motion :
S = ut + (1/2)a$t^2$
105 = -4t + (1/2(10$t^2$)
105 = -4t + 5$t^2$
5$t^2$- 4t - 105 = 0
t = 5 and -4.2 seconds.
Since time is always positive, t = 5 s.