Barron's 2nd Edition PT1 Q16

Barron's Book

16) This problem asks us the effect on the maximum height of a projectile if its speed is doubled. We are first told that the ball reaches a max height h when the initial speed is v.

Let's start by choosing the kinematic equation we will use.

Where d is distance, v[o] is initial velocity, v[f] is final velocity, t is time, and a is acceleration

When a projectile reaches its max height, its y-component of velocity is 0. The problem tells us that the ball is thrown straight up, so the x-component of velocity is also 0. We will just focus on the y-component from here on.

For this problem, it would be best to use the third equation because at max height we know that change in displacement will be h, v[f] will be 0, v[o] will be 0, and a will be -g.

Where v is velocity, g is acceleration of gravity, and h is height

Now, we have an equation representing the situation described. the problem asks what will be the maximum height if the initial speed is doubled.

Where v is velocity, g is acceleration of gravity, and h is height

First, I found out that by doubling the speed, you are multiplying the left side of the equation by 4. In order to balance the equation, it is necessary to multiply the right side by 4. Finally, I brought the constant to the height because that is the only value that could be affected by doubling the speed; the acceleration of gravity is held constant.

Answer: D