Projectile Motion

One example of projectile motion often seen in movies are car and motorcycle jumps. One classic example of this is in the movie The Blues Brothers (1980). Jake and Elwood Blues are stuck in traffic because a drawbridge is opening. Deciding not to wait they skip the line and jump the open drawbridge. The actual bridge used in the jump is the 95th St. Bridge in Chicago.

How fast must the Blues Brothers be driving to make that jump?
Solution: The 95th St. Bridge in Chicago has a length of 105m. In the film it looks like the angle the raised bridge halves make with the horizontal is about 45\deg. If that’s the case the x-component would be \frac{1}{2}(105m)\cos{(45)}= 37m. Thus the open distance between the two bridge halves would be 105m-2(37m) = 31m, which is the distance the car must travel in the x direction to make it across the bridge. In the y direction the car will leave the bridge with some positive y component of its velocity going up, but gravity will accelerate the car down until eventually the car is back at the same height. In order to make the jump the car must travel the 31m in the x direction before the car has returned to its original y velocity. Thus we can write

y = v_{0}\sin{(45)} t - \frac{1}{2}g t^2 = 0
x = v_{0}\cos{(45)} t = 31m.

Solving the first equation for v_0 gives

v_0 = \frac{1}{2}{g\over{\sin{(45)}}}t.

Solving the x equation for t gives

t = {31m \over{v_0 \cos{(45)}}}

which we can plug into the expression for v_0 to give

v_0^2 = \frac{1}{2}{(9.81 m/s^2)(31m)\over{\sin{(45)}\cos{(45)}}} = 304 m^2/s^2.

So v_0 = 17.4m/s or 39 mph a very reasonable speed for a car. However, we have neglected air resistance so you would probably want to be about 10 mph faster than this to be safe. The problem with jumping bridges in a car is not the speed you need to attain, but the landing. Stunt cars have much stronger tires and shocks so that that can survive the landing and keep on driving. A normal car could jump the bridge, but would likely blow out the tires and shocks on the landing.

Another example can be seen in the movie 2 Fast 2 Furious (2003) which features a double car jump.