A stuntman drives a motorcycle off a 350 m cliff going 70 mph. The angle of elevation of the cliff is 21 degree. He is hoping to make it across a 261 m wide river and land on a ledge 82 m high. Does he make it?

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See previous post: Wed,10-15-14, 6:23 AM

2. An astronaut in orbit outside an orbiting space station throw her 800.0-g camera away in disgust when it jams. If she and her space suit together have a mass of 100.0 kg and the speed of the camera is 12.0 m/s.

To determine whether the stuntman makes it across the river and lands on the ledge, we need to calculate the horizontal distance covered by the motorcycle when it reaches the same vertical height as the ledge.

1. Calculate the time it takes for the motorcycle to fall off the cliff:
Since we are given the initial speed of the motorcycle (70 mph), we need to convert it to meters per second (m/s):
70 mph = 31.29 m/s

Using the formula s = ut + (1/2)at², where s is the vertical distance (350 m), u is the initial vertical velocity (0 m/s), and a is the acceleration due to gravity (-9.8 m/s²), we can solve for t:
350 = 0t + (1/2)(-9.8)t²
350 = -4.9t²
t² = 350 / (-4.9)
t² ≈ -71.43
Since time cannot be negative, there is an error in the calculation. This means that the motorcycle cannot fall off the cliff.

Therefore, the stuntman does not make it across the river and land on the ledge.

To determine whether the stuntman can make it across the river and land on the ledge, we need to analyze the trajectory of the motorcycle. Let's break down the problem into smaller steps:

Step 1: Calculate the horizontal distance traveled by the motorcycle.
To calculate this distance, we can use the formula:
Horizontal distance = Speed × Time

Since the motorcycle is traveling at 70 mph, we need to convert this to meters per second:
1 mph = 0.447 m/s (approximately)

Therefore, the speed of the motorcycle is:
Speed = 70 mph × 0.447 m/s = 31.29 m/s (approximately)

Now, we can determine the time of flight using the formula:
Time = Horizontal distance / Speed

Given that the river width is 261 m and the stuntman wants to land on the ledge, it means the total horizontal distance required is 261 + 82 = 343 m (261 m across the river + 82 m on the ledge).

So, the time of flight is:
Time = 343 m / 31.29 m/s = 10.96 s (approximately)

Step 2: Calculate the vertical component of the motorcycle's velocity.
Since we know the angle of elevation of the cliff is 21 degrees, we can calculate the vertical component of the velocity using trigonometry.

Vertical velocity = Speed × sin(angle)

Vertical velocity = 31.29 m/s × sin(21 degrees) = 10.75 m/s (approximately)

Step 3: Calculate the time taken for the motorcycle to reach maximum height.
The motorcycle will reach its maximum height when its vertical velocity reaches zero. We can use the formula:

Time to reach maximum height = Vertical velocity / acceleration due to gravity

In this case, acceleration due to gravity is approximately 9.8 m/s².

Time to reach maximum height = 10.75 m/s / 9.8 m/s² = 1.10 s (approximately)

Step 4: Calculate the time taken for the motorcycle to fall from maximum height to the ledge.
The vertical distance to be covered is 82 m.

Using the kinematic equation:
Vertical distance = (1/2) × acceleration due to gravity × time²

Rearranging the equation to solve for time:
Time = √(2 × Vertical distance / acceleration due to gravity)

Time = √(2 × 82 m / 9.8 m/s²) = √(16.73 s²) = 4.09 s (approximately)

Step 5: Calculate the total time taken for the motorcycle to travel horizontally and reach the ledge.
Total time = Time of flight + Time to reach maximum height + Time from maximum height to ledge

Total time = 10.96 s + 1.10 s + 4.09 s = 16.15 s (approximately)

Finally, we can compare the total time taken with the time required to calculate whether the stuntman makes it across the river and lands on the ledge. If the total time is less than or equal to 16.15 s, then the stuntman makes it; otherwise, he doesn't make it.

Now you have all the necessary calculations to determine whether the stuntman succeeds.