A daredevil jumps a canyon 10.6 m wide. To do so, he drives a car up a 19° incline. (The daredevil lands on the other side of the canyon at the same elevation as takeoff.)
What minimum speed must he achieve to clear the canyon?
I DON'T KNOW!!! I'M LOOKING FOR THAT ANSWER AS WELL!!!
To determine the minimum speed required to clear the canyon, we can use the principles of projectile motion. Let's break down the problem step by step:
Step 1: Identify the known values:
- Width of the canyon (d) = 10.6 m
- Angle of the incline (θ) = 19°
- Vertical displacement (Δy) = 0 (since the daredevil lands at the same elevation as takeoff)
Step 2: Split the initial velocity into horizontal and vertical components:
Since the daredevil wants to clear the canyon horizontally, we only need to consider the vertical component. The horizontal component of velocity will not affect the jump distance.
Step 3: Calculate the vertical component of velocity:
To calculate the vertical component, we can use the formula: v_y = v * sin(θ), where v_y represents the vertical component of velocity and θ is the angle of the incline.
Step 4: Determine the time of flight:
Since the daredevil lands at the same elevation, the time it takes for the jump will be the same as the time it takes for the fall. We can find the time of flight using the formula: t = 2 * (v_y / g), where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 5: Calculate the horizontal distance:
The horizontal distance covered by the daredevil can be calculated using the formula: d_x = v * cos(θ) * t, where d_x represents the horizontal distance and θ is the angle of the incline.
Step 6: Set up the equation for clearing the canyon:
To clear the canyon, the horizontal distance covered should be equal to or greater than the width of the canyon. Therefore, we can set up the equation: d_x ≥ d.
Step 7: Solve the equation for velocity:
Rearrange the equation d_x = v * cos(θ) * t and substitute the value of t from step 4 to find the minimum velocity required: v = (d / (cos(θ) * t)).
Now, we can plug in the values and calculate the minimum velocity required to clear the canyon.