First slide

Projectile motion

Question

Two boats both having a mass of 150 kg including passengers in it are at rest. A sack of mass 50 kg makes 1st boat having total mass of 200 kg. It is thrown to the second boat with a velocity whose horizontal component is $2 {ms}^{- 1}$ , relative to water. Calculate the distance (in m) between the boat 8.5 s. after the throw if the sack spent 0.5 s in air. Neglect the resistance of air and water.

Difficult

Solution

First boat
$0 = 50 \times 2 + 150 v$
$v_{1} = - \frac{2}{3} {ms}^{- 1}$
Second boat
$100 = 200 v_{2}$
$v_{2} = \frac{1}{2} {ms}^{- 1}$
$T = \frac{2 u_{y}}{g} = 0 .5 u_{y} = 2 .5 {ms}^{- 1}$
Initial distance $= \frac{2 \times 2 .5 \times 2}{10} = 1 m$
Distance $= u_{rel} \times t = (\frac{1}{2} + \frac{2}{3}) \times 8$
Total distance = 8 m

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