(a) daredevil is attempting to jump his motorcycle over a line of buses parked end to end by driving up a 32° ramp at a speed of 4-0.0 m/s (14-4- km/h), How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are 20.0 m long?
L=vₒ²•sin2α/g = 40²•sin64º/9.8=146.74 m
146.74/20 =7.34 => 7 buses
7 buses
To find out how many buses Daredevil can clear, we need to determine the distance he can jump based on his speed and the angle of the ramp.
Here's how you can calculate it:
Step 1: Convert the speed from km/h to m/s.
- Given: Speed = 40.0 km/h = 40.0 m/s
Step 2: Calculate the horizontal velocity component.
- Horizontal velocity = Speed * cos(angle)
- Given: angle = 32°
- Calculate: Horizontal velocity = 40.0 m/s * cos(32°)
Step 3: Calculate the time of flight.
- Time of flight = (2 * vertical velocity) / gravitational acceleration
- Given: Gravitational acceleration = 9.8 m/s^2
- Calculate: Vertical velocity = Speed * sin(angle)
- Calculate: Time of flight = (2 * Speed * sin(angle)) / gravitational acceleration
Step 4: Calculate the horizontal distance traveled.
- Horizontal distance = Horizontal velocity * Time of flight
Step 5: Determine the number of buses cleared.
- Given: Length of each bus = 20.0 m
- Calculate: Number of buses cleared = Horizontal distance / Length of each bus
Let's plug in the values and calculate:
Step 1: Speed = 40.0 km/h = 40.0 m/s
Step 2: Horizontal velocity = 40.0 m/s * cos(32°)
Step 3: Vertical velocity = 40.0 m/s * sin(32°)
- Time of flight = (2 * Vertical velocity) / 9.8 m/s^2
Step 4: Horizontal distance = Horizontal velocity * Time of flight
Step 5: Number of buses cleared = Horizontal distance / 20.0 m
By following these steps and performing the calculations, you can determine the number of buses Daredevil can clear with his motorcycle jump.