a playe rthrows ball from a height of 1.5 m above ground above ground with intiial velocity of 20 m/s
at an angle of 60.
the time req. tp hit the walll and at what height
no idea. how far away is the wall?
To find the time required for the ball to hit the wall and at what height, we can use the equations of motion.
First, let's break down the motion of the ball into horizontal and vertical components.
Horizontal Component:
The initial horizontal velocity of the ball is given as 20 m/s. Since there are no external forces acting horizontally, the horizontal velocity remains constant throughout the motion. Therefore, the time taken to hit the wall would be the distance to the wall divided by the horizontal velocity.
Vertical Component:
The initial vertical velocity of the ball can be found by multiplying the initial velocity (20 m/s) by the sine of the launch angle (60°). So, the vertical component of the initial velocity becomes 20 m/s * sin(60°) = 17.32 m/s.
Now, let's find the time taken for the ball to hit the ground. We can use the equation of motion for vertical motion:
h = ut + (0.5) * g * t^2
where h is the height, u is the initial velocity, g is the acceleration due to gravity (approximately -9.8 m/s^2), and t is the time taken.
We know that the initial height (h) is 1.5 m, the initial vertical velocity (u) is 17.32 m/s, and g is -9.8 m/s^2. We need to find the time (t).
Substituting the given values into the equation, we get:
1.5 = (17.32 * t) + (0.5 * -9.8 * t^2)
Simplifying the equation:
0.5 * -9.8 * t^2 + 17.32 * t + 1.5 = 0
This equation is a quadratic equation. We can solve it using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Where a, b, and c are coefficients as follows:
a = 0.5 * -9.8 = -4.9
b = 17.32
c = 1.5
Now, substitute the values into the quadratic formula to get the solutions for t. The positive solution would represent the time taken for the ball to hit the ground.
Once you have the time taken for the ball to hit the ground, multiply it by the horizontal velocity to get the distance to the wall.
To find the height at which the ball hits the wall, we can use the equation:
height = initial height + (vertical component of initial velocity * t) + (0.5 * g * t^2)
Substitute the known values to find the height at which the ball hits the wall using the time calculated earlier.
Following these steps, you should be able to find the time required to hit the wall and the height at which it hits the wall.