agent dave, flying a constant 215 km/hr horizontally in a low - flying helicopter wants to drop a small explosive onto a master criminal automobile travelling 155km/hr on a level highway 78m below. At what angle (with the horizontal) should the car be in his sights when the bomb is released
To determine the angle at which Agent Dave should aim the bomb, we need to consider the horizontal and vertical components of the helicopter's and the car's motion.
First, let's examine the horizontal motion:
- The helicopter is flying at a constant speed of 215 km/hr horizontally.
- The car is traveling at a speed of 155 km/hr on the level highway.
Since both the helicopter and the car are moving horizontally, there is no relative horizontal motion between them. Therefore, we can ignore the horizontal component in our calculations.
Now, let's focus on the vertical motion:
- The car is at a height of 78m below the helicopter.
- We need to determine the angle at which the bomb should be released from the helicopter to hit the car.
To solve this problem, we can break it down into two separate motions: the bomb's vertical motion (free fall) and the car's vertical motion (due to its speed).
For the bomb's vertical motion:
Using the equations of motion, we can calculate the time it takes for the bomb to fall from the helicopter to the level of the car:
h = (1/2) * g * t^2
Where:
h is the height (78m in this case),
g is the acceleration due to gravity (9.8 m/s^2),
t is the time.
Simplifying the equation:
78 = (1/2) * 9.8 * t^2
156 = 9.8 * t^2
t^2 = 156 / 9.8
t^2 = 15.9184
t ≈ 3.99 seconds
Now, considering the car's vertical motion:
During the time it takes for the bomb to fall from the helicopter to the level of the car (approximately 3.99 seconds), the car would have moved a certain distance downward due to its speed.
Vertical distance traveled by the car = speed * time
= 155 km/hr * (3.99 seconds / 3600 seconds/hr)
≈ 0.43 m
Therefore, the car would have moved approximately 0.43 meters downwards during the time it takes for the bomb to fall.
To determine the angle, we can use the inverse tangent function:
angle = arctan(78m / 0.43m)
≈ 89.97 degrees
Therefore, Agent Dave should aim the bomb at an angle of approximately 90 degrees (or straight down) in his sights when he releases it to hit the car.