Final answer:
To find the height of the building from which a ball is dropped and hits the ground with a 30 m/s velocity, we use the kinematic equation for free fall. The calculated height is approximately 45.92 m, making option (d) 45 m the correct answer.
Step-by-step explanation:
The question is related to the physics of free fall and projectile motion. To determine the height of the building from which the ball is dropped and strikes the ground with an impact velocity of 30 m/s, we can use the kinematic equation of motion for free fall without air resistance
v^2 = u^2 + 2gh
Where v is the final velocity (30 m/s), u is the initial velocity (0 m/s since the ball is dropped), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the building. Plugging in the values:
30^2 = 0 + 2(9.8)h
900 = 19.6h
h = 900 / 19.6 = 45.92 m
Thus, the correct answer is (d) 45 m, as it is the closest value without exceeding the calculated height.