Question

A ball of mass m is tossed straight up and reaches a height of 15 ft. What is the mass of the ball?

Answer 1

To determine the mass of the ball tossed straight up, additional information such as the initial velocity or kinetic energy is required; the given height alone (15 ft) is insufficient to calculate the mass.

Step-by-step explanation:

To find the mass of the ball, we need more information. The height reached by the ball is related to the initial velocity, launch angle, and gravitational acceleration. If we assume that the ball is launched vertically upward and neglect air resistance, we can use the following kinematic equation:

h = 1/2 g t^2

where:

- h is the height reached (15 ft),

- g is the acceleration due to gravity (approximately (32 ft/s^2) on Earth),

- t is the time of flight.

Assuming the ball is thrown vertically upward and then falls back down, the total time of flight is twice the time it takes to reach the maximum height.

Let's denote the initial velocity as v_0 , and the time of flight as t. The equation for the height becomes:

h = v_0 t - 1/2 g t^2

At the maximum height, the final velocity is 0, so v_0 = gt. Substituting this into the height equation gives:

h = 1/2 g t^2

Now we can solve for t using the given height:

15 = 1 / 2 x 32 x t^2

Solve for \(t\), and then use v_0 = gt to find the initial velocity. Once you have the initial velocity, you can find the kinetic energy using the formula KE = 1/2 m v_0^2. However, to find the mass m, you would need additional information, such as the kinetic energy of the ball. If you have the kinetic energy, you can use the formula to solve for the mass.

Answer 2

The mass of the ball cannot be determined from the height it reaches alone, as mass is an intrinsic property and additional information is required to calculate it.

Step-by-step explanation:

The mass of the ball tossed straight up that reaches a height of 15 ft is not directly influenced by the height it reaches. Instead, the mass of the ball can be found using kinematic equations if information such as the initial velocity and the force applied is known. However, the given question does not provide sufficient information to calculate the mass of the ball, since mass is an intrinsic property and is not determined by the motion of the object or its height reached during that motion.