Suppose David Ortiz hits a home run which travels 361. feet (110. m). Assuming it left the bat at 50.°, how fast was it hit?
To calculate the velocity of the home run hit by David Ortiz, we can use the basic principles of projectile motion and trigonometry.
The initial velocity of the ball can be decomposed into vertical and horizontal components. The vertical component determines the height the ball reaches, while the horizontal component determines its range or distance traveled.
We are given that the ball traveled a distance of 110. m horizontally, which indicates the horizontal component of velocity. Therefore, we need to find the magnitude of the initial velocity (v) which is the sum of its horizontal (v_x) and vertical (v_y) components.
Let's start by finding v_x using the cosine function:
v_x = v * cos(θ)
Where:
v_x is the horizontal component of velocity
v is the magnitude of the initial velocity
θ (theta) is the launch angle, given as 50°
Now, let's substitute the value of v_x into the equation for range:
range = v_x * time
Since time is not given, we need to determine it. The range (R) of the projectile is the horizontal distance traveled. In this case, it is given as 361. feet (110. m). To calculate time, we can use the equation:
time = distance / v_x
Now, we can substitute the known values into our equations and solve for the magnitude of the initial velocity (v):
v_x = v * cos(50°)
time = 110. m / v_x
Finally, we can calculate the magnitude of the initial velocity (v) using the following equation:
v = range / (cos(θ) * time)
Now, let's plug in the values and calculate the result:
v = 110. m / (cos(50°) * (110. m / v_x))
Note: Make sure to convert the angle to radians when using trigonometric functions.
After performing the calculations, the resulting value of v will give us the speed at which David Ortiz hit the home run.
separate the initial velocity into vertical and horizontal components.
Viv=Vsin50
Vih=Vcos50
horizontaldistance=Vih*t
solve for t.
Now,
you know the vertical distance..
Hf=Hi+Viv*t-1/2 g t^2
where Viv=Vsin50
solve for V.