Question

The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank is cm. (Take g = 10 m/s²).

Answer 1

Correct Answer: 2000

To determine the range of the ball thrown upwards from the boat as observed by a stationary observer on the riverbank, follow these steps:

1. Calculate total velocities:
   • Boat velocity in still water: 27 km/h. Convert to m/s: \(27 \times \frac{1000}{3600} = 7.5\) m/s.
   • River velocity: 9 km/h. Convert to m/s: \(9 \times \frac{1000}{3600} = 2.5\) m/s.
   • Boat's velocity relative to the riverbank (downstream): \(7.5 + 2.5 = 10\) m/s.
   • Ball's horizontal velocity relative to the riverbank (same as boat): 10 m/s. Ball's vertical velocity: 10 m/s upwards.
2. Calculate the ball's time of flight:
   • Time to reach maximum height using \(v = u + gt\): \(0 = 10 + (-10)t \Rightarrow t = 1\) s.
   • Total time of flight (up and down): \(2 \times 1 = 2\) s.
3. Calculate the observed range:
   • Range = Horizontal velocity × Time of flight = \(10 \text{ m/s} \times 2 \text{ s} = 20\) m.
   • Convert range to centimeters: \(20\) m = \(2000\) cm.

The observed range of the ball from the riverbank is 2000 cm.