a parachutist of total mass 75 kg jumps from an aeroplane moving at a speed of 60m/s at a height of 900 m above the ground. Her parachute reduce the speed of descent to 5m/s. calculate the decrease in her gravitational potential energy store as a result of her descent.
PE = mgh
h = 900-60t
To calculate the decrease in the parachutist's gravitational potential energy, we can use the formula:
ΔPE = mgh,
where:
ΔPE is the change in gravitational potential energy,
m is the mass of the parachutist (75 kg),
g is the acceleration due to gravity (approximately 9.8 m/s²),
and h is the change in height.
The parachutist falls from a height of 900 m to the ground, which means the change in height is -900 m (negative because she is descending).
Now we can substitute these values into the formula:
ΔPE = (75 kg) × (9.8 m/s²) × (-900 m).
ΔPE = -661,500 Joules.
Therefore, the decrease in the parachutist's gravitational potential energy store as a result of her descent is -661,500 Joules. Note that the negative sign indicates a decrease in potential energy.
To calculate the decrease in gravitational potential energy, we first need to find the initial gravitational potential energy at the height of 900m above the ground.
The formula for gravitational potential energy is given by:
Potential Energy = mass × gravity × height
Here, the mass of the parachutist is 75 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the height is 900m. Let's substitute these values into the formula:
Initial Potential Energy = 75 kg × 9.8 m/s^2 × 900 m
Now, we can calculate the initial potential energy:
Initial Potential Energy = 661,500 J
Next, we need to find the final gravitational potential energy at the height of 900m above the ground with a decreased speed of 5 m/s. Since the speed is reduced, the parachutist is moving slower and therefore has less kinetic energy. The decrease in kinetic energy is converted to potential energy.
The formula for kinetic energy is given by:
Kinetic Energy = 0.5 × mass × velocity^2
Initially, the parachutist was moving at a speed of 60 m/s, and after the parachute opens, the speed reduces to 5 m/s. Using the formula, we can find the initial and final kinetic energies:
Initial Kinetic Energy = 0.5 × 75 kg × (60 m/s)^2
Final Kinetic Energy = 0.5 × 75 kg × (5 m/s)^2
Now, let's calculate the initial and final kinetic energies:
Initial Kinetic Energy = 135,000 J
Final Kinetic Energy = 937.5 J
The decrease in gravitational potential energy is equal to the increase in kinetic energy. Hence:
Decrease in Potential Energy = Initial Potential Energy - Final Potential Energy
Decrease in Potential Energy = 661,500 J - (937.5 J + 135,000 J)
Decrease in Potential Energy = 525,563.5 J
Therefore, the decrease in the parachutist's gravitational potential energy store as a result of her descent is approximately 525,563.5 Joules.