Two bodies A and B are projected upwards such that the velocity of A is double the velocity of B. Then, the ratio of heights to which body A and body B will rise is:a.8:1b.1:8c.1:4d.4: 1
Question
Two bodies A and B are projected upwards such that the velocity of A is double the velocity of B. Then, the ratio of heights to which body A and body B will rise is:a.8:1b.1:8c.1:4d.4: 1
Solution
The height to which a body rises when projected upwards is given by the formula:
h = u^2 / 2g
where: h is the height, u is the initial velocity, g is the acceleration due to gravity.
Given that the velocity of A is double the velocity of B, we can denote the velocity of B as u and the velocity of A as 2u.
Therefore, the height to which A will rise is:
h_A = (2u)^2 / 2g = 4u^2 / 2g = 2u^2 / g
And the height to which B will rise is:
h_B = u^2 / 2g
The ratio of the heights to which A and B will rise is therefore:
h_A / h_B = (2u^2 / g) / (u^2 / 2g) = 2 / 0.5 = 4
So, the correct answer is d. 4:1.
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