Final answer:
To find the vertical velocity at the point of impact, we use the equation v_final = sqrt(2gh), where g is the acceleration due to gravity and h is the height of the cliff. The total velocity at the point of impact can be found by dividing the distance traveled by the time taken. The angle of impact can be calculated using trigonometry with the equation tan(angle) = vertical velocity / horizontal velocity.
Step-by-step explanation:
To find the answers to the given questions, we can use the equations of motion to analyze the vertical and horizontal components of the car's motion. Let's start by calculating the vertical velocity at the point of impact.
- Since the car falls straight off the cliff, the initial vertical velocity is zero and the final vertical velocity can be found using the equation: v_final = sqrt(2gh), where g is the acceleration due to gravity and h is the height of the cliff. Plugging in the values, we get v_final = sqrt(2 * 9.8 * 54) m/s.
- Next, to find the total velocity at the point of impact, we need to find the horizontal velocity. Since the only force acting on the car is gravity, which only affects the vertical component, the horizontal velocity remains constant. So, the horizontal velocity at the point of impact is the same as the horizontal component of the initial velocity, which is the distance traveled divided by the time taken. Plugging in the values, we get horizontal velocity = 130 m / 2 s.
- Finally, to find the angle of impact, we can use trigonometry. The angle of impact can be found using the equation: tan(angle) = vertical velocity / horizontal velocity. Plugging in the values, we get tan(angle) = sqrt(2 * 9.8 * 54) m/s / (130 m / 2 s). Solving for the angle, we get angle = arctan(sqrt(2 * 9.8 * 54) m/s / (130 m / 2 s)).