really stuck, a 90 kg skier has 140 KJ of total mechanical energy when he is at a height of 120m above the bottom of the hill. calculate the skiers kinetic energy. calculate his speed?
To calculate the skier's kinetic energy, we need to find the potential energy at the top of the hill and subtract it from the total mechanical energy.
Potential Energy (PE) = mass (m) * gravity (g) * height (h)
Using the given values:
Mass (m) = 90 kg
Gravity (g) = 9.8 m/s²
Height (h) = 120 m
PE = m * g * h
= 90 kg * 9.8 m/s² * 120 m
= 105120 J (Joules)
Now, to find the skier's kinetic energy, we can subtract the potential energy from the total mechanical energy:
Total Mechanical Energy = Potential Energy (PE) + Kinetic Energy (KE)
Given:
Total Mechanical Energy = 140 kJ = 140,000 J (since 1 kJ = 1000 J)
140,000 J = 105,120 J + KE
Solving for KE:
KE = 140,000 J - 105,120 J
= 34,880 J (Joules)
The skier's kinetic energy is 34,880 J.
To determine the skier's speed, we can use the equation:
Kinetic Energy (KE) = 0.5 * mass (m) * velocity² (v²)
Rearranging the equation:
v² = (2 * KE) / m
Plugging in the known values:
v² = (2 * 34,880 J) / 90 kg
= 775.11 m²/s²
To find the speed (v), we take the square root of v²:
v = √(775.11 m²/s²)
= 27.84 m/s
Therefore, the skier's speed is 27.84 m/s.