A ball is dropped from a height. What is the height of the building if it takes 4 seconds to reach the ground? Also, what is the initial speed required to throw a ball to a maximum height of 100m?

Question

Asked on March 31, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

Accepted Answer · 2026-03-31T15:20:45.403Z

Step 1: Identify the given values and the formula for free fall. For an object dropped from rest, the initial velocity u = 0 m/s. The time taken to reach the ground t = 4 s. The acceleration due to gravity g = 9.8 m/s^2. The formula for the distance (height) is h = ut + (1)/(2)gt^2. Step 2: Substitute the values into the formula and calculate the height. h = (0 m/s)(4 s) + (1)/(2)(9.8 m/s^2)(4 s)^2 h = 0 + (1)/(2)(9.8 m/s^2)(16 s^2) h = (4.9 m/s^2)(16 s^2) h = 78.4 m The height of the building is 78.4 m. The correct option is (d). d) 78.4 m Step 1: Identify the given values and the formula for vertical motion. The maximum height attained h = 100 m. At the maximum height, the final velocity v = 0 m/s. The acceleration due to gravity g = -9.8 m/s^2 (negative because it opposes the upward motion). The formula relating initial velocity, final velocity, acceleration, and displacement is v^2 = u^2 + 2gh. Step 2: Substitute the values into the formula and solve for the initial speed u. 0^2 = u^2 + 2(-9.8 m/s^2)(100 m) 0 = u^2 - 1960 m^2/s^2 u^2 = 1960 m^2/s^2 u = sqrt(1960 m)^2/s^2 u ≈ 44.27 m/s Rounding to one decimal place, the initial speed is 44.3 m/s. Comparing with the options, 44.2 m/s is the closest. The correct option is (b). b) 44.2 m/s Step 1: Identify the given values and the formula for weight. The mass of the man m = 60 kg. The acceleration due to gravity on Earth g_E = 9.8 m/s^2. The acceleration due to gravity on the Moon g_M = (g_E)/(6). The formula for weight is W = mg. Step 2: Calculate the acceleration due to gravity on the Moon. g_M = 9.8 m/s^26 ≈ 1.633 m/s^2 Step 3: Calculate the weight of the man on the Moon. W_M = m × g_M W_M = 60 kg × 1.633 m/s^2 W_M = 97.98 N Rounding to the nearest whole number, the weight is approximately 98 N. The correct option is (d). d) 98 N Step 1: Identify the given values and the formula for weight. The weight of the object on Earth W_E = 196 N. The acceleration due to gravity on Earth g_E = 9.8 m/s^2. The formula for weight is W = mg. Step 2: Rearrange the formula to solve for mass and substitute the values. m = (W_E)/(g_E) m = 196 N9.8 m/s^2 m = 20 kg The mass of the object is 20 kg. 20 kg

Accepted Answer · 2026-03-31T15:20:45.403Z

Step 1: Identify the given values and the formula for free fall. For an object dropped from rest, the initial velocity u = 0 m/s. The time taken to reach the ground t = 4 s. The acceleration due to gravity g = 9.8 m/s^2. The formula for the distance (height) is h = ut + (1)/(2)gt^2. Step 2: Substitute the values into the formula and calculate the height. h = (0 m/s)(4 s) + (1)/(2)(9.8 m/s^2)(4 s)^2 h = 0 + (1)/(2)(9.8 m/s^2)(16 s^2) h = (4.9 m/s^2)(16 s^2) h = 78.4 m The height of the building is 78.4 m. The correct option is (d). d) 78.4 m Step 1: Identify the given values and the formula for vertical motion. The maximum height attained h = 100 m. At the maximum height, the final velocity v = 0 m/s. The acceleration due to gravity g = -9.8 m/s^2 (negative because it opposes the upward motion). The formula relating initial velocity, final velocity, acceleration, and displacement is v^2 = u^2 + 2gh. Step 2: Substitute the values into the formula and solve for the initial speed u. 0^2 = u^2 + 2(-9.8 m/s^2)(100 m) 0 = u^2 - 1960 m^2/s^2 u^2 = 1960 m^2/s^2 u = sqrt(1960 m)^2/s^2 u ≈ 44.27 m/s Rounding to one decimal place, the initial speed is 44.3 m/s. Comparing with the options, 44.2 m/s is the closest. The correct option is (b). b) 44.2 m/s Step 1: Identify the given values and the formula for weight. The mass of the man m = 60 kg. The acceleration due to gravity on Earth g_E = 9.8 m/s^2. The acceleration due to gravity on the Moon g_M = (g_E)/(6). The formula for weight is W = mg. Step 2: Calculate the acceleration due to gravity on the Moon. g_M = 9.8 m/s^26 ≈ 1.633 m/s^2 Step 3: Calculate the weight of the man on the Moon. W_M = m × g_M W_M = 60 kg × 1.633 m/s^2 W_M = 97.98 N Rounding to the nearest whole number, the weight is approximately 98 N. The correct option is (d). d) 98 N Step 1: Identify the given values and the formula for weight. The weight of the object on Earth W_E = 196 N. The acceleration due to gravity on Earth g_E = 9.8 m/s^2. The formula for weight is W = mg. Step 2: Rearrange the formula to solve for mass and substitute the values. m = (W_E)/(g_E) m = 196 N9.8 m/s^2 m = 20 kg The mass of the object is 20 kg. 20 kg

A ball is dropped from a height. What is the height of the building if it takes 4 seconds to reach the ground? Also, what is the initial speed required to throw a ball to a maximum height of 100m?

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A ball is dropped from a height. What is the height of the building if it takes 4 seconds to reach the ground? Also, what is the initial speed required to throw a ball to a maximum height of 100m?

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