A motorcycle stunt rider must jump a 100m wide canyon given a 20° ramp positioned on either side. What minimum speed is required so the rider will clear the canyon?

Vicos20*timeinair=101meters

solve for time in air.

hf=hi+viSin30*timeinair-4.9time^2
solve for vi. Hf=hi=0

50 m/s

To determine the minimum speed required for the motorcycle stunt rider to clear the canyon, we need to consider the range of the jump.

The range of the jump can be calculated using the horizontal motion equation:

Range = (Initial Velocity^2 * sin(2θ)) / g

where:
- Initial Velocity is the speed of the motorcycle
- θ is the angle of the ramp (20°)
- g is the acceleration due to gravity (9.8 m/s^2)

We want the range to be equal to or greater than the width of the canyon (100m). So we can set up the equation:

100 = (Initial Velocity^2 * sin(2*20°)) / 9.8

Let's solve for the Initial Velocity:

Initial Velocity^2 = (100 * 9.8) / sin(40°)

Initial Velocity^2 = 980 / sin(40°)

Initial Velocity = √(980 / sin(40°))

Using a scientific calculator, we can find:

Initial Velocity ≈ 28.9 m/s

Therefore, the minimum speed required for the rider to clear the canyon is approximately 28.9 m/s.

To calculate the minimum speed required for the motorcycle stunt rider to clear the 100m wide canyon, we can use the principles of projectile motion.

Step 1: Break down the problem into horizontal and vertical components.
The horizontal component is the distance the motorcycle needs to travel, which is 100m. The vertical component is the height the motorcycle needs to reach to clear the canyon, which can be calculated based on the angle of the ramp.

Step 2: Calculate the vertical component.
To calculate the vertical component, we can use the formula for the maximum height reached in projectile motion:

H = (v^2 * sin^2(θ)) / (2g)

where H is the maximum height, v is the initial velocity, θ is the angle of the ramp, and g is the acceleration due to gravity (approximately 9.8 m/s^2).

In this case, we want the maximum height to be equal to the width of the canyon, so we have:

100 = (v^2 * sin^2(20°)) / (2 * 9.8)

Step 3: Solve for the minimum speed.
Rearranging the equation, we can solve for the minimum speed (v):

v^2 = (100 * 2 * 9.8) / sin^2(20°)

Taking the square root of both sides, we get:

v = sqrt((100 * 2 * 9.8) / sin^2(20°))

Now, we can use any scientific calculator or an online calculator to find the value of v. Plugging in the numbers will give us the minimum speed required for the motorcycle stunt rider to clear the canyon.