A Dare daredevil wants to jump his motorcycle across a 50 m Canyon
a) If his speed is 30m/s and a ramp angle is 50 degrees where should the landing ramp be placed?
b) With the same ramp what initial speed should he have if the landing ramp is 10 m from the far edge
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To find the answers to these questions, we can use projectile motion equations. Let's break it down step by step:
a) To determine where the landing ramp should be placed, we need to find the horizontal distance the daredevil would cover given his speed and the ramp angle.
First, let's calculate the time it takes for the daredevil to cross the canyon. We'll use the horizontal component of the velocity and the distance:
Horizontal distance (d) = speed (v) * time (t*cosθ)
In this case, the distance is given as 50 m, and the speed is 30 m/s, so we have:
50 m = 30 m/s * t * cos(50°)
To find the time it takes, we rearrange the equation:
t = 50 m / (30 m/s * cos(50°))
Now, let's calculate the vertical distance the daredevil would travel. We'll use the vertical component of the velocity, the time, and the acceleration due to gravity (9.8 m/s^2):
Vertical distance (h) = v * t * sinθ - 0.5 * g * t^2
In this case, the speed is 30 m/s, the time can be calculated from the previous step, the angle is 50°, and the acceleration due to gravity is 9.8 m/s^2:
h = 30 m/s * t * sin(50°) - 0.5 * 9.8 m/s^2 * t^2
Now, let's find the distance from the near edge of the canyon to the landing ramp. We can use the horizontal component of the velocity and the time:
Landing ramp distance (d_landing) = speed (v) * time (t)* sinθ
In this case, the speed is 30 m/s, and the time can be calculated from the first step:
d_landing = 30 m/s * t * sin(50°)
b) To find the initial speed needed to reach the desired landing ramp distance, we need to reverse the process and solve for the speed.
We'll use the same calculations as in part a), but now the distance from the near edge to the landing ramp is given as 10 m.
First, we find the time it takes to cross the canyon:
time (t) = d_landing / (speed (v) * sinθ)
Given that d_landing is 10 m, the angle is still 50°, and we want to solve for the speed:
v = d_landing / (t * sin(50°))
Now, you can use these equations to find the answers to a) and b) using the given values for speed and ramp angle.