How to Calculate Minimum Speed for a Car to Jump Over Cars

Calculating Minimum Speed for Car Jumping Over Cars

To calculate the minimum speed the stunt driver must drive off the horizontal ramp to clear 8 cars parked side by side, we can use principles of projectile motion. We need to find the initial horizontal velocity (\(v_0\)) required.

The horizontal distance the car must clear (\(d\)) is 22 meters, and the vertical height of the ramp (\(h\)) is 1.5 meters.

We can use the following equation for horizontal motion: \[d = v_0 t\]

Where \(t\) is the time of flight. We also need to find the time of flight, which is the time it takes for the car to reach the ground from the top of the ramp. We can use the vertical motion equation: \[h = \frac{1}{2} g t^2\]

Rearrange the second equation to solve for \(t\): \[t = \sqrt{\frac{2h}{g}}\]

Now, substitute this expression for \(t\) into the first equation: \[d = v_0 \sqrt{\frac{2h}{g}}\]

Solve for \(v_0\): \[v_0 = \frac{d}{\sqrt{\frac{2h}{g}}}\]

Substitute the known values: \[v_0 = \frac{22 \, \text{m}}{\sqrt{\frac{2 \times 1.5 \, \text{m}}{9.81 \, \text{m/s}^2}}}\]