A hailstorm causes an average pressure of 1.4 N/m² on the 200-m² flat roof of a house. The hailstones, each of mass 7.0 × 10^-³ kg, have an average velocity of 10 m/s perpendicular to the roof and rebound after hitting the roof with the same speed. How many hailstones hit the roof each second?

Question

Quizplus · Accepted Answer

The force exerted by each hailstone on the roof can be found using the formula F = ma, where F is the force, m is the mass, and a is the acceleration. Since the hailstones rebound with the same speed, their acceleration is equal to their initial velocity divided by the time taken to come to a stop and change direction.

The time taken for a hailstone to hit the roof and rebound can be found using the vertical motion equation:

h = (1/2)gt^2

where h is the height of the roof (200 m), g is the acceleration due to gravity (9.8 m/s^2), and t is the time taken for the hailstone to hit the roof and rebound. Solving for t, we get:

t = sqrt(2h/g) = sqrt(400/9.8) = 6.42 s

The velocity of each hailstone can be expressed as the distance it travels divided by the time it takes:

v = 2h/t = 62.1 m/s

Therefore, the acceleration of each hailstone is:

a = v/t = 9.67 m/s^2

The force exerted by each hailstone on the roof is:

F = ma = (7.0 × 10^-3 kg) * (9.67 m/s^2) = 6.76 × 10^-2 N

The number of hailstones hitting the roof per second can be found by dividing the total force exerted on the roof by the force exerted by each hailstone:

N = (1.4 N/m^2)/(6.76 × 10^-2 N) = 20.71...

Rounding down to the nearest whole number, we get:

N = 20 hailstones/s = 2000 hailstones/s

Therefore, the answer is choice B.

A Hailstorm Causes an Average Pressure of 1