In the latest Indian Jones film, Indy is supposed to throw a grenade from his car, which is going 93.0 km/h, to his enemy's car, which is going 130km/h. The enemy's car is 17.0m in front of the Indy's when he lets go of the grenade.
1)If Indy throws the grenade so its initial velocity relative to him is at an angle of 45above the horizontal, what should the magnitude of the initial velocity be? The cars are both traveling in the same direction on a level road. You can ignore air resistance.
2)Find the magnitude of the velocity relative to the earth.
To find the magnitude of the initial velocity of the grenade relative to Indy, we can use the relative velocity concept. The relative velocity is the difference in velocities between the two cars.
1) First, we need to find the relative velocity of Indy's car with respect to the enemy's car. Since they are both traveling in the same direction, we subtract their velocities:
Relative velocity = Velocity of enemy's car - Velocity of Indy's car
Relative velocity = 130 km/h - 93.0 km/h
Relative velocity = 37 km/h
2) Now that we have the relative velocity, we can break it down into horizontal and vertical components. Given that the angle of the initial velocity relative to Indy is 45 degrees above the horizontal, we can use trigonometry to find the components.
The horizontal component (Vx) of the initial velocity can be found using the formula:
Vx = V * cos(θ)
where V is the magnitude of the initial velocity and θ is the angle.
Vx = V * cos(45°) -- (1)
The vertical component (Vy) of the initial velocity can be found using the formula:
Vy = V * sin(θ)
where V is the magnitude of the initial velocity and θ is the angle.
Vy = V * sin(45°) -- (2)
3) We need to find the time taken by the enemy's car to cover the distance between the enemy's car and Indy's car. This can be done using the formula:
time = distance / relative velocity
time = 17.0 m / (37 km/h * 1000 m/km * 1/3600 h/s)
Note: We convert km/h to m/s by multiplying by (1000 m/km)/(3600 s/h).
4) Now that we have the time, we can calculate the horizontal displacement (x) of the grenade relative to Indy using the formula:
x = Vx * time
5) Finally, we can calculate the magnitude of the initial velocity (V) by using the Pythagorean theorem:
V = sqrt(x^2 + y^2)
To find the magnitude of the velocity relative to the earth, we need to consider the horizontal motion of the grenade relative to Indy's initial position.
1) The horizontal component of the velocity (Vx) remains the same as calculated earlier.
2) The vertical component of the velocity (Vy) is now the relative velocity between the grenade and the Earth. Since there is no vertical acceleration, Vy remains constant.
3) To find the magnitude of the velocity relative to the Earth, we once again use the Pythagorean theorem:
Magnitude of velocity relative to Earth = sqrt(Vx^2 + Vy^2)
By following these steps, you can find the answers to both questions in the problem.