A baseball player slams a fastball towards left field. The ball is hit 1.00 m above the plate at an initial velocity of 36.0 m/s at a 30 degree angle above the horizontal. The left field wall is 113 m away and is 3.00 m high. Is this a home run shot or not?.
find time in to go 113 m
113=vihoriz(t) solve for time t.
Now , consider the verical height.
hf=hi+vivert*t-4.9t^2 compute hf. is it over 3 m?
To determine whether the baseball hit is a home run or not, we need to calculate the range and height of the ball's trajectory.
Step 1: Calculate the horizontal range:
The horizontal range can be found using the time of flight of the ball. We can calculate the time it takes for the ball to reach the left field wall using the horizontal component of the initial velocity.
Horizontal component of initial velocity (Vx) = V * cos(theta)
where V is the initial velocity and theta is the angle above the horizontal.
Vx = 36.0 m/s * cos(30 degrees) ≈ 31.18 m/s
Now, we can use this horizontal component of velocity to calculate the time of flight (t):
Range (R) = Vx * t
113 m = 31.18 m/s * t
t ≈ 3.62 s
Step 2: Calculate the maximum height:
The maximum height can be found using the vertical component of initial velocity.
Vertical component of initial velocity (Vy) = V * sin(theta)
Vy = 36.0 m/s * sin(30 degrees) ≈ 18.00 m/s
The time taken to reach the maximum height (t_max) can be calculated using the following formula:
Vy_max = Vy – g * t_max
0 = 18.00 m/s – 9.8 m/s^2 * t_max
t_max ≈ 1.84 s
Now, we can calculate the maximum height (H_max) using the formula:
H_max = Vy * t_max - 0.5 * g * t_max^2
H_max = 18.00 m/s * 1.84 s - 0.5 * 9.8 m/s^2 * (1.84 s)^2
H_max ≈ 18.76 m
Step 3: Determine if it's a home run:
To determine if it's a home run, we need to check if the ball's range (113 m) is greater than the distance to the outfield wall and if the maximum height (18.76 m) is higher than the height of the wall (3.00 m).
Since the range (113 m) is greater than the distance to the wall and the maximum height (18.76 m) is higher than the height of the wall, we can conclude that it is a home run shot.
In summary, based on the calculations, the baseball player hit a home run.