If a person jumps 8.59m horizontelly and jumps at 23 degrees, what is his initial velocity? Plz and thank you.
8.59=v*cos23*time
in the vertical
0=v*sin23*t-1/2 g t^2
t= 2v*sin23/g
put that value of t in the first equation, solve for v.
To determine the initial velocity of a person who jumps horizontally and at an angle, we can break down the motion into horizontal and vertical components.
Given:
Horizontal distance = 8.59m
Launch angle = 23 degrees
Step 1: Calculate the horizontal component of the initial velocity.
The horizontal component remains constant throughout the motion, so we can use the formula:
Horizontal distance = Horizontal velocity × Time
Assuming there is no air resistance, there is no horizontal force acting on the person. Therefore, the initial horizontal velocity (Vx) remains the same as the final horizontal velocity. Since the person jumps horizontally, the horizontal distance is equal to the initial horizontal velocity multiplied by the time of flight.
Horizontal distance (d) = Vx × Time (t)
Since the person is only jumping horizontally, the vertical distance is zero. Therefore, the total time of flight is the same as the time taken for the vertical motion.
Vertical distance (Vy) = V0y × Time (t)
0 = V0y × t
Therefore, the total time of flight (t) can be determined from the vertical motion using the formula:
Vy = V0y - g × t
Given that the vertical distance (Vy) is zero when the person lands, we can rearrange the formula:
0 = V0y - g × t
t = V0y / g
Step 2: Calculate the vertical component of the initial velocity.
Since the launch is at an angle, we can find the vertical component of the initial velocity (V0y) using the formula:
V0y = V0 × sin(θ)
Where:
V0 is the initial velocity
θ is the launch angle
Step 3: Substitute the values into the equations and solve for V0.
Substituting the calculated value of t in Step 1 into the equation for Vy, we get:
0 = V0y - g × t
Substituting the value of V0y from Step 2 into the above equation:
0 = (V0 × sin(θ)) - g × (V0y / g)
0 = (V0 × sin(23)) - V0y
Thus, by substituting the known values (θ = 23 degrees, g = 9.8 m/s²), we can solve the equation to find the initial velocity (V0).