A person is riding a bicycle at a constant speed of 36 km h ⁻¹ along a straight horizontal road. A ball is dropped from a window of a building exactly when the bicycle is at a horizontal distance of 30 m from the drop point. If the ball lands directly in the bicycle's front basket, what is the height of the window from the ground? (Given g = 10 m s ⁻² and neglect the height of the basket from the ground)

Step-by-step solution

The speed of the bicycle is v = 36 km h ⁻¹ = 36 5 18 m s ⁻¹ = 10 m s ⁻¹ . The time taken by the bicycle to cover the horizontal distance of 30 m is: t = d v = 30 10 = 3 s For the ball to land in the basket, the time of free fall must be equal to the time taken by the bicycle to reach the drop point. Using the equation of motion for the vertically dropped ball ( u = 0 ): h = 1 2 gt^2 h = 1 2 10 (3)^2 = 5 9 = 45 m Answer: 45 m