I am so confused on this one.
In 1975, coming out of retirement, the daredevil Evel Knievel successfully jumped over 14 Greyhound buses (a total of 40.5m). To do so, he drives his motorcycle up an incline at a speed of 44.7m/s (about 100mi/hr). What minimum angle should the ramp be in order to clear the buses?
assuming the end of the ramp is at the same height as the tops of the buses, you just need to solve for θ using the range:
v^2/g sin2θ >= 40.5
To determine the minimum angle required for Evel Knievel to clear the buses, we can use the following principles of projectile motion:
1. The horizontal distance covered by the motorcycle can be calculated using the formula: horizontal distance = initial velocity * time of flight.
2. The time of flight can be calculated using the formula: time of flight = 2 * (initial vertical velocity) / acceleration due to gravity.
3. The initial vertical velocity can be calculated using the equation: vertical velocity = initial velocity * sin(theta), where theta is the angle of the ramp.
4. The initial horizontal velocity remains constant throughout the motion and is equal to the horizontal component of the initial velocity: horizontal velocity = initial velocity * cos(theta).
To calculate the minimum angle needed, we need to find the angle at which the horizontal distance covered by the motorcycle is equal to or greater than the total length of the buses (40.5m).
Let's calculate it step by step:
1. Calculate the time of flight:
Using the formula mentioned above, time of flight = 2 * (initial vertical velocity) / acceleration due to gravity.
Since the motorcycle's initial vertical velocity is equal to the vertical component of the initial velocity, we can calculate it as: vertical velocity = initial velocity * sin(theta).
Substitute the given values, initial velocity = 44.7m/s and acceleration due to gravity would be 9.8m/s^2.
Time of flight = 2 * (initial velocity * sin(theta)) / acceleration due to gravity.
2. Calculate the horizontal distance covered:
Using the formula mentioned above, horizontal distance = initial velocity * time of flight.
Substitute the given values, initial velocity = 44.7m/s and time of flight is provided from the previous calculation.
3. Compare the horizontal distance with the length of the buses:
If the horizontal distance is equal to or greater than the length of the buses (40.5m), then the angle of the ramp is sufficient. If it is smaller, then the angle needs to be increased.
Repeat steps 1-3 for different angles until you find the minimum angle that allows the motorcycle to clear the buses.
Keep in mind that this calculation assumes ideal projectile motion without accounting for factors like air resistance and any loss of speed during the jump.