Physics Problem: Height of Cliff Calculation

Question:

A stunt car traveling at 20 m/s flies horizontally off a cliff and lands 39.2 m from the base of the cliff. How tall is the cliff? Choose from the following options: a) 78.4 meters b) 98.0 meters c) 196 meters d) 294 meters
Final answer:

Using principles of horizontal projectile motion, the stunt car's vertical displacement can be calculated with the equation h = 0.5gt^2. The time taken to hit the ground is calculated using the horizontal motion (t = d/v). Hence the height of the cliff is around 18.85 meters, which does not match with any of the provided options.

Answer:

To determine the height of the cliff, we can use physics principles related to horizontal projectile motion. In horizontal projectile motion such as a stunt car flying off a cliff, the horizontal motion and vertical motion are independent of each other. The stunt car has an initial horizontal velocity of 20 m/s and it has traveled 39.2m horizontally when it lands. However, the question is asking for the height (vertical distance) of the cliff. Since there's no initial vertical velocity for the stunt car (it flies horizontally off the cliff), we can refer to the equation h = 0.5gt^2 where h represents the height, g is the acceleration due to gravity (which is approximately 9.8 m/s² in the absence of air resistance), and t is the time it takes for the car to hit the ground. We need to find the time first. We can do this by using the horizontal motion. We know that the horizontal distance traveled by the car (d) = velocity (v) x time (t). We can rearrange this equation to determine the time: t = d/v = 39.2 m / 20 m/s = 1.96 s. Substituting t into the equation for vertical motion, we find that the height h is given by h = 0.5*9.8 m/s²*(1.96 s)^2 = 18.85 m. Therefore none of the options given (78.4 meters, 98.0 meters, 196 meters, 294 meters) are correct. The closest option would be 78.4 meters but it's way off the accurate answer.

Projectile motion is a fascinating topic in physics that deals with the motion of objects thrown or projected into the air. When an object is launched into the air with an initial velocity, it follows a curved path known as a trajectory, influenced by both horizontal and vertical forces. In the case of the stunt car flying off a cliff, the horizontal motion of the car remains constant at 20 m/s, as no horizontal forces are acting on it once it leaves the cliff. However, the vertical motion is affected by the force of gravity, causing the car to accelerate downwards.

To calculate the height of the cliff, we separate the horizontal and vertical components of motion. The horizontal velocity of 20 m/s allows us to determine the time it takes for the car to hit the ground by dividing the horizontal distance traveled (39.2 m) by the horizontal velocity. This gives us a time of 1.96 seconds.

Next, we focus on the vertical motion using the equation h = 0.5gt^2, where h is the height of the cliff, g is the acceleration due to gravity (9.8 m/s²), and t is the time taken to hit the ground (1.96 s). Substituting the values into the equation, we find that the height of the cliff is approximately 18.85 meters, which does not match any of the given options.

Therefore, understanding the principles of projectile motion and the separation of horizontal and vertical components are essential in solving such problems. By applying these concepts, we can accurately calculate the height of the cliff in this scenario, even if the provided options do not align with the calculated value.