Question

A ball of mass 0.100 kg is thrown into the air with a speed of 6.0 m/s and from a height of 2.0m. What is the mechanical energy of the ball when it has a height of 5.0 m.

Answer 1

v(t) = 6-9.8t

h(t) = 2+6t-4.9t^2
find t when h=5, and then figure the energy for that velocity and height.

Answer 2

V^2 = Vo^2+2g*h = 0

6^2+(-19.6)h = 0
h max. = 1.84 m above launching point. = 3.84 m above gnd.
Therefore, 6 m/s initial velocity is not high enough for the ball
to reach 5 m.

Answer 3

[AI-generated answer — Explain Bot]

To find the mechanical energy of the ball when it has a height of 5.0 m, we need to consider both its kinetic energy and its potential energy at that height.

1. Start by calculating the initial potential energy of the ball when it is at a height of 2.0 m. The potential energy (PE) of an object at a height h is given by the equation: PE = mgh, where m is the mass (0.100 kg) of the ball, g is the acceleration due to gravity (9.8 m/s²), and h is the height (2.0 m).

PE(initial) = (0.1 kg) × (9.8 m/s²) × (2.0 m) = 1.96 Joules

2. Next, calculate the initial kinetic energy (KE) of the ball using its speed (6.0 m/s) and mass (0.100 kg). The kinetic energy of an object is given by the equation: KE = 0.5 × m × v², where m is the mass and v is the velocity.

KE(initial) = 0.5 × (0.1 kg) × (6.0 m/s)² = 1.8 Joules

3. Now, find the potential energy of the ball at a height of 5.0 m using the same equation as step 1.

PE(final) = (0.1 kg) × (9.8 m/s²) × (5.0 m) = 4.9 Joules

4. Since the ball is in the air and there is no external force acting on it (ignoring air resistance), the total mechanical energy (E) of the ball is conserved. So the mechanical energy at any height will be the sum of its initial potential energy and initial kinetic energy.

E(initial) = PE(initial) + KE(initial) = 1.96 Joules + 1.8 Joules = 3.76 Joules

5. Therefore, the mechanical energy of the ball when it has a height of 5.0 m is equal to the sum of its initial potential energy and initial kinetic energy.

E(final) = PE(final) + KE(initial) = 4.9 Joules + 1.8 Joules = 6.7 Joules

So the mechanical energy of the ball when it has a height of 5.0 m is 6.7 Joules.