A body with a mass of 2 tonnes is moving at 100 km/h. What is the maximum vertical height it can climb before coming to rest?

A body with a mass of 2 tonnes is moving at 100 km/h. What is the maximum vertical height it can climb before coming to rest?

• A. 27.8 km
• B. 5.10 m
• C. 1.41 m
• D. 39.3 m

Answer: (D)

To determine the maximum vertical height that a body can climb before coming to rest, we can utilize the principle of conservation of energy. This principle states that the kinetic energy of the moving body will be converted into gravitational potential energy as it ascends a height. First, we calculate the kinetic energy of the body using the formula: \[ \text{Kinetic Energy} (KE) = \frac{1}{2} m v^2 \] Where: - \( m \) is the mass (in kilograms), - \( v \) is the velocity (in meters per second). Since the mass of the body is given as 2 tonnes, we convert it to kilograms: \[ 2 \, \text{tonnes} = 2000 \, \text{kg} \] Next, we convert the speed from kilometers per hour to meters per second: \[ 100 \, \text{km/h} = \frac{100 \times 1000}{3600} \approx 27.78 \, \text{m/s} \] Now, substituting the values into the kinetic energy equation: \[ KE = \frac{1}{2} \times 2000 \, \text{kg

To determine the maximum vertical height that a body can climb before coming to rest, we can utilize the principle of conservation of energy. This principle states that the kinetic energy of the moving body will be converted into gravitational potential energy as it ascends a height.

First, we calculate the kinetic energy of the body using the formula:

[ \text{Kinetic Energy} (KE) = \frac{1}{2} m v^2 ]

Where:

• ( m ) is the mass (in kilograms),

• ( v ) is the velocity (in meters per second).

Since the mass of the body is given as 2 tonnes, we convert it to kilograms:

[ 2 , \text{tonnes} = 2000 , \text{kg} ]

Next, we convert the speed from kilometers per hour to meters per second:

[ 100 , \text{km/h} = \frac{100 \times 1000}{3600} \approx 27.78 , \text{m/s} ]

Now, substituting the values into the kinetic energy equation:

[ KE = \frac{1}{2} \times 2000 , \text{kg