What is the distance from the base of the cliff where a 1500 kg car lands after being propelled off a 30-meter-high cliff at a speed of 25 m/s with an incline of 20 degrees?
Calculating Car Landing Distance
Final answer: The car, being propelled off a cliff at an inclined angle, will land approximately 58 meters away from the base of the cliff as calculated via breaking down the car's velocity into horizontal and vertical components and applying laws of motion.
Explanation:
The scenario involves a stunt man driving a 1500 kg car at a speed of 25 m/s off a 30-meter-high cliff. The road leading to the cliff is inclined upward at an angle of 20 degrees. To determine the distance the car lands from the base of the cliff, we need to analyze the motion of the car.
First, let's calculate the vertical and horizontal initial velocities of the car after being propelled off the cliff. With the incline at an angle of 20 degrees, we can use trigonometric functions to find the vertical (Vy) and horizontal (Vx) components of the velocity:
\[V_y = V \times \sin(θ) = 25 \times \sin(20) ≈ 8.5 m/s\]
\[V_x = V \times \cos(θ) = 25 \times \cos(20) ≈ 23.4 m/s\]
The vertical velocity component, Vy, will keep the car airborne, while the horizontal velocity component, Vx, will determine the horizontal distance traveled.
Next, to find the time the car is in the air, we can utilize the second equation of motion for the vertical motion. At the top of the car’s trajectory, the vertical velocity becomes zero. Therefore, we can calculate the time the car spends in the air:
\[t = (2 \times h) / g = (2 \times 30) / 9.8 ≈ 2.47 s\]
Finally, to determine how far from the base of the cliff the car lands, we multiply the time spent in the air by the horizontal velocity:
\[x = V_x \times t = 23.4 \times 2.47 ≈ 57.8 m\]
Therefore, the car will land approximately 58 meters from the base of the cliff.
For further understanding of Projectile Motion, you can explore additional resources or information on related topics.