A projectile is launched at an angle of 34.0o above the horizontal. The projectile has a mass of 1.50 kg and is given an initial speed of 20.0 m/s. a) What is the initial kinetic energy of the projectile? b) By how much does the gravitational potential energy of the projectile change as the projectile moves from its initial position to the highest vertical point in its motion? c) What is the maximum height reached by the projectile?

Question

A projectile is launched at an angle of 34.0o above the horizontal. The projectile has a mass of 1.50 kg and is given an initial speed of 20.0 m/s. a) What is the initial kinetic energy of the projectile? b) By how much does the gravitational potential energy of the projectile change as the projectile moves from its initial position to the highest vertical point in its motion? c) What is the maximum height reached by the projectile?

Answer 1

(a)

KE=(1/2)mv²

(b)
At maximum height,
KE in y-direction = 0, i.e.
loss in KE
=(1/2)m(v sin(θ))²

(c)
Maximum height, h
equate mgh to loss in KE, or
mgh = (1/2)m(v sin(θ))²

Solve for h.

Answer 2

a) To find the initial kinetic energy of the projectile, we can use the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Given:
Mass (m) = 1.50 kg
Velocity (v) = 20.0 m/s

We can now substitute the given values into the formula:

Kinetic Energy = (1/2) * 1.50 kg * (20.0 m/s)^2

Kinetic Energy = (1/2) * 1.50 kg * 400 m^2/s^2

Kinetic Energy = 300 J (Joules)

Therefore, the initial kinetic energy of the projectile is 300 Joules.

b) The change in gravitational potential energy as the projectile moves from its initial position to the highest vertical point in its motion can be calculated using the formula:

Change in Gravitational Potential Energy = mass * g * change in height

Given:
Mass (m) = 1.50 kg
Change in height = maximum height reached by the projectile
Acceleration due to gravity (g) = 9.8 m/s^2

Since the projectile starts and ends at the same height, the change in height is zero. Therefore:

Change in Gravitational Potential Energy = 1.50 kg * 9.8 m/s^2 * 0

Change in Gravitational Potential Energy = 0 J (Joules)

Therefore, the change in gravitational potential energy is zero.

c) The maximum height reached by the projectile can be found by analyzing the projectile's motion. At the highest point, the vertical component of the projectile's velocity becomes zero.

To find the maximum height, we can use the formula for vertical displacement:

Vertical Displacement = (v_initial * sin(theta))^2 / (2 * g)

Given:
Initial velocity (v_initial) = 20.0 m/s
Angle above the horizontal (theta) = 34.0 degrees
Acceleration due to gravity (g) = 9.8 m/s^2

First, convert the angle from degrees to radians:

theta_radians = 34.0 * (pi/180)

Next, substitute the given values into the formula:

Vertical Displacement = (20.0 * sin(34.0))^2 / (2 * 9.8)

Vertical Displacement = (20.0 * 0.559193)^2 / (2 * 9.8)

Vertical Displacement = 4.716 m

Therefore, the maximum height reached by the projectile is 4.716 meters.