A projectile is launched with a speed of 41 m/s at an angle of 55° above the horizontal. Use conservation of energy to find the maximum height reached by the projectile during its flight.
Maximum height is achieved when the vertical velocity component, V sin 55 = 0
The kinetic energy loss at that time, which is due to the vertical component only, equals the potential energy gain.
(M/2) (Vsin55)^2 = M g H
H = (Vsin55)^2/(2g)
To find the maximum height reached by the projectile, we can use the principle of conservation of energy.
Step 1: Identify the initial and final states of the projectile.
In this case, the initial state is when the projectile is launched, and the final state is when the projectile reaches its maximum height.
Step 2: Determine the types of energy involved.
The energy involved in the projectile's motion is kinetic energy (KE) and gravitational potential energy (PE).
Step 3: Apply the conservation of energy principle.
According to the conservation of energy principle, the total energy of the system remains constant.
At the initial state, the projectile has only kinetic energy, given by KE_initial = 1/2 * m * v_initial^2, where v_initial is the initial velocity of the projectile.
At the final state (maximum height), the projectile has only potential energy, given by PE_final = m * g * h, where m is the mass of the projectile, g is the acceleration due to gravity, and h is the maximum height reached.
Using the conservation of energy principle, we have:
KE_initial = PE_final
1/2 * m * v_initial^2 = m * g * h
Step 4: Solve for the maximum height.
Rearrange the equation to solve for h:
h = (1/2 * v_initial^2) / g
Substituting the given values:
h = (1/2 * (41 m/s)^2) / 9.8 m/s^2
Calculating:
h = (1/2 * (1681 m^2/s^2)) / 9.8 m/s^2
h = 86.12 meters
Therefore, the maximum height reached by the projectile is 86.12 meters.