a football is thrown to a moving receiver .the football leaves the quarterback's hands 1.75m above the ground with a velocity of 17.0m/s[25deg]if the receiver starts 12.0m away from the quarterback along the line of flight of the ball when is is thrown , what constant velocity must she have to get to the ball at the instant it is 1.75 m above the ground ?
See previous post,4:21 PM.
To solve this problem, we need to find the constant velocity of the receiver required to catch the ball at the instant it is 1.75m above the ground.
First, let's break down the given information:
Initial height of the ball (above the ground) = 1.75m
Initial velocity of the ball = 17.0m/s [25°]
Distance between the receiver and quarterback when the ball is thrown = 12.0m
To find the constant velocity of the receiver, we can use the equation of motion:
Δx = V₀ * t + 0.5 * a * t²
Where:
Δx = displacement (distance between the receiver and quarterback when the ball is caught)
V₀ = initial velocity of the receiver
t = time taken to reach the ball
In this case, the acceleration (a) can be assumed to be zero because there is no vertical acceleration acting on the ball during its flight.
Let's break the velocity of the ball into horizontal and vertical components.
Horizontal component of the initial velocity (V₀x) = V₀ * cos(angle)
Vertical component of the initial velocity (V₀y) = V₀ * sin(angle)
Now, we know that the displacement in the x-direction is the distance between the receiver and the quarterback (12.0m). Therefore, we can write:
Δx = V₀x * t
Substituting V₀x = V₀ * cos(angle), we get:
12.0 = V₀ * cos(angle) * t --------- Equation 1
Similarly, in the y-direction, we know that the displacement is the difference between the initial height of the ball (1.75m) and the receiver's height (zero). So, we have:
-1.75 = V₀y * t + 0.5 * (-9.8) * t²
Substituting V₀y = V₀ * sin(angle) and simplifying, we get:
-1.75 = V₀ * sin(angle) * t - 4.9 * t² --------- Equation 2
We have two equations (Equation 1 and Equation 2) with two unknowns: V₀ and t.
Solving these equations simultaneously will give us the values of V₀ and t.
Once we have the value of t, we can substitute it back into Equation 1 to find the constant velocity of the receiver (V₀).