Bubba is driving his other truck across his farm and finds that there is a gulch blocking his path. The ground leading up to the edge of the gulch is sloped upwards by 24.2°. The gulch is 3.13 meters wide. The far side of the gulch is 1.15 meters higher than the near side. Bubba decides to jump the gulch in his truck like is often done on his favorite TV show. He drives up the incline and launches across the gulch with an initial velocity of 7.42 m/s.
How much above or below the other side of the gulch are Bubba's tires when he reaches the far side of his jump.
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To find out how much above or below the other side of the gulch Bubba's tires are when he reaches the far side of his jump, we need to break down the problem into different steps.
Step 1: Calculate the horizontal distance traveled by Bubba's truck across the gulch.
Since Bubba launches across the gulch with an initial velocity of 7.42 m/s, we can calculate the time it takes for him to travel from the near side to the far side of the gulch using the equation:
Time = Distance / Velocity
The distance is given as 3.13 meters, and the velocity is 7.42 m/s. Thus:
Time = 3.13 m / 7.42 m/s
Step 2: Calculate the vertical distance (height) Bubba's truck reaches during the jump.
To calculate the height, we can use the equation for vertical displacement:
Displacement = Initial Velocity * Time + (1/2) * Acceleration * Time^2
The initial velocity is 0 m/s since Bubba starts from the bottom of the incline, and the acceleration is due to gravity (-9.8 m/s^2). However, we need to find the time it takes for Bubba's truck to travel from the bottom of the incline to the point where it launches.
To find the time, we can use the relation between distance (s), initial velocity (u), acceleration (a), and angle of incline (θ):
s = (u^2 * sin(2θ)) / g
Here, u = 7.42 m/s, θ = 24.2°, and g = 9.8 m/s^2.
Substituting the given values, we can solve for the distance traveled along the incline:
s = (7.42^2 * sin(2 * 24.2°)) / 9.8
Step 3: Calculate the total vertical displacement or height over the gulch.
The total vertical displacement is given as 1.15 meters higher on the far side of the gulch than on the near side.
Total Vertical Displacement = Height on Far Side - Height on Near Side
To calculate the height on the near side, we need to find the vertical component of the incline:
Height on Near Side = Height of Incline * cos(θ)
Here, the height of the incline is given as 3.13 m * sin(24.2°).
Finally, we can calculate the total vertical displacement:
Total Vertical Displacement = Height of Incline * cos(θ) + 1.15 meters
Combining all these steps, you can solve for the total vertical displacement, which will give you the answer to the question.