Which of the following has a higher kinetic energy?
A 1000 kg car rolling at a speed of 5 m/s across the floor or a 1500 kg hippo swimming at a speed of 2 m/s
a
the hippo
b
their kinetic energies are equal
c
not enough information to determine
d
the car
The answer is d. The kinetic energy of an object is given by the formula KE=0.5mv^2, where m is the mass of the object and v is its velocity. Based on this formula, the kinetic energy of the car would be higher than that of the hippo. This is because even though the hippo has a greater mass, its velocity is much lower than that of the car, resulting in a lower kinetic energy.
To compare the kinetic energies, we can use the formula for kinetic energy:
Kinetic energy (KE) = 0.5 * mass * velocity^2
For the car:
Mass of the car = 1000 kg
Velocity of the car = 5 m/s
For the hippo:
Mass of the hippo = 1500 kg
Velocity of the hippo = 2 m/s
Let's calculate the kinetic energy for each:
For the car:
KE_car = 0.5 * 1000 kg * (5 m/s)^2
= 0.5 * 1000 kg * 25 m^2/s^2
= 12500 kg m^2/s^2
For the hippo:
KE_hippo = 0.5 * 1500 kg * (2 m/s)^2
= 0.5 * 1500 kg * 4 m^2/s^2
= 3000 kg m^2/s^2
Comparing the two kinetic energies, we find that the kinetic energy of the car is higher than the kinetic energy of the hippo:
KE_car > KE_hippo
Therefore, the correct answer is (d) the car.
To determine which object has a higher kinetic energy, we need to understand the equation for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Let's calculate the kinetic energy for each object and compare them:
For the car:
Mass (m) = 1000 kg
Velocity (v) = 5 m/s
KE(car) = 1/2 * 1000 kg * (5 m/s)^2 = 1/2 * 1000 kg * 25 m^2/s^2 = 12,500 kg m^2/s^2
For the hippo:
Mass (m) = 1500 kg
Velocity (v) = 2 m/s
KE(hippo) = 1/2 * 1500 kg * (2 m/s)^2 = 1/2 * 1500 kg * 4 m^2/s^2 = 3,000 kg m^2/s^2
Comparing the two values, we can see that the car has a higher kinetic energy of 12,500 kg m^2/s^2, while the hippo has a kinetic energy of 3,000 kg m^2/s^2.
Therefore, the correct answer is (d) the car has a higher kinetic energy.