daredevil jumps 10m wide. he drives a car up a 11 degree incline. what was minimum speed to clear the 10m? acceleration is 9.81
To find the minimum speed required for Daredevil to clear the 10m gap, we can use the principles of projectile motion.
First, let's break down the problem into horizontal and vertical components. The horizontal component involves the 10m gap, while the vertical component involves the 11-degree incline.
1. Vertical Component:
The vertical motion is influenced by gravity and the incline. We can find the vertical velocity (Vy) at the end of the jump by calculating the vertical displacement using the equation:
d = (V^2 - V0^2) / (2 * a)
where:
- d is the vertical displacement (equal to 10m)
- V is the final vertical velocity at the peak (equal to 0 m/s, as Daredevil would momentarily reach the top)
- V0 is the initial vertical velocity
- a is the acceleration (equal to 9.81 m/s^2)
Substituting the values into the equation, we have:
10 = (0 - V0^2) / (2 * 9.81)
Simplifying the equation, we get:
0 - V0^2 = 196.2
V0^2 = -196.2
As we don't have a negative velocity, we can ignore the negative sign. Thus, we have:
V0 = √(196.2)
≈ 14.0 m/s
2. Horizontal Component:
Since there is no horizontal force acting on the car, the horizontal velocity (Vx) remains constant throughout the jump. We want to find the minimum initial horizontal velocity (V0x) required to clear the 10m gap.
We can use the equation:
d = V0x * t
where:
- d is the horizontal displacement (equal to 10m)
- V0x is the initial horizontal velocity
- t is the time taken for the car to travel horizontally
To find t, we need to know the time of flight of the projectile. The time of flight can be determined using the equation:
t = 2 * Vy / a
Substituting the known values:
t = 2 * 14.0 / 9.81
≈ 2.85s
Now, we can substitute the values of d and t into the equation:
10 = V0x * 2.85
Simplifying the equation, we get:
V0x = 10 / 2.85
≈ 3.51 m/s
Therefore, the minimum speed (V0x) that Daredevil needs to clear the 10m gap is approximately 3.51 m/s.