The best leaper in the animal kingdom is the puma, which can jump to a height of 12.4 ft when leaving the ground at an angle of 38°. With what speed, in SI units, must the animal leave the ground to reach that height?
change ft to m.
Vf^2=Vi^2+2gd
0=(VSin38)^2+2(-9.8)h
solve for V
19
To determine the required speed for a puma to reach a certain height, we need to apply principles of projectile motion. We can use basic kinematic equations to solve for the initial velocity (speed) of the puma.
Given:
Height (h) = 12.4 ft = 3.779 m (converted to SI units)
Angle (θ) = 38°
The key concept to remember is that the vertical and horizontal motions of the puma are independent of each other. Thus, we can break down the initial velocity into its vertical and horizontal components.
Step 1: Calculate the vertical component of the initial velocity (Vy):
Using the equation: Vy = V * sin(θ)
where V represents the initial velocity (speed).
Vy = V * sin(38°)
Step 2: Calculate the time (t) it takes for the puma to reach the peak height:
Using the equation: h = (Vy^2) / (2 * g)
where g represents the acceleration due to gravity, approximately 9.8 m/s^2.
3.779 = (Vy^2) / (2 * 9.8)
Simplify the equation to solve for Vy^2: Vy^2 = 3.779 * 2 * 9.8
Step 3: Solve for Vy:
Take the square root of both sides: Vy = √(3.779 * 2 * 9.8)
Step 4: Calculate the horizontal component of the initial velocity (Vx):
Using the equation: Vx = V * cos(θ)
Step 5: Solve for V:
Since V represents the initial velocity, it remains the same for both the vertical and horizontal components. Therefore, we can use either Vy or Vx to find V.
Vy = V * sin(38°) → V = Vy / sin(38°)
Step 6: Substitute the values and calculate V:
V = (√(3.779 * 2 * 9.8)) / sin(38°)
After substituting the values and evaluating the equation using a calculator, we find that the puma must leave the ground with an initial speed of approximately 13.29 meters per second (m/s) to reach a height of 12.4 ft.