A home run is hit such a way that the baseball just clears a wall 26 m high located 114 m from home plate. The ball is hit at an angle of 35â—¦ to the horizontal, and air resistance is negligible. Assume the ball is hit at a height of 2 m above the ground.
What is the initial speed of the ball? The acceleration of gravity is 9.8 m/s2 .
Answer in units of m/s.
How much time does it take for the ball to reach the wall?
Answer in units of s.
Find the speed of the ball when it reaches the wall.
Answer in units of m/s.
35 degrees*
a. Range = Vo^2*sin(2A)/g.
114 = Vo^2*sin(70)/9.8,
Vo = 34.5 m/s.
b. Xo = Vo*cos35 = 34.5*cos35 = 28.2 m/s. = Hor. component.
Yo = 34.5*sin35 = 19.8 m/s = Ver. component.
Y = Yo + g*Tr.
0 = 19.8 -9.8Tr,
Tr = 2.02s. = Rise time. = Time to reach the wall.
h = ho + Yo*Tr + 0.5g*Tr^2.
h = 2 + 19.8*2.02 - 4.9*2.02^2 = 22m above gnd. = max ht.
If the max. ht. is 22 m, the wall can't
be 26 m high. Check the given ht.
c. Assuming the ball is at max. ht. when it reaches the wall:
V = Xo + Yi = 28.2 + 0i = 28.2 m/s.
To answer these questions, we will use the principles of projectile motion and the equations of motion.
1. Finding the initial speed of the ball:
The initial velocity of the ball can be separated into two components: the horizontal component (Vx) and the vertical component (Vy). We can find the initial speed (V0) by using the given angle and the horizontal and vertical components.
Vx = V0 * cos(angle)
Vy = V0 * sin(angle)
Given that the ball is hit at an angle of 35 degrees, we can substitute the values into the equations:
Vx = V0 * cos(35°)
Vy = V0 * sin(35°)
2. Finding the time it takes for the ball to reach the wall:
We can use the horizontal component of the velocity (Vx) and the distance to the wall to calculate the time (t) it takes for the ball to reach the wall. The equation used is:
distance = velocity * time
114 m = Vx * t
By substituting the value of Vx:
114 m = V0 * cos(35°) * t
Now, we can solve for time (t).
3. Finding the speed of the ball when it reaches the wall:
To find the final speed of the ball when it reaches the wall, we need to calculate the final vertical velocity (Vfy). We can use the equation:
Vfy = Vy + (acceleration * time)
Since there is no vertical acceleration (neglecting air resistance) and the initial vertical velocity (Vy) is known, the final vertical velocity (Vfy) will be equal to the initial vertical velocity. Hence,
Vfy = Vy = V0 * sin(angle)
So, once we have the initial speed of the ball (V0) and the vertical velocity (Vy), we can find the speed of the ball when it reaches the wall by calculating the magnitude of the final velocity, which is given by:
Vfinal = sqrt(Vx^2 + Vfy^2)
Now, let's plug in the values and calculate the answers.
Once we calculate the values for each question, we can provide the final answers.