An athlete thtrew a short put of mass7.52kg through a distance of 24m when we projected a short put at angle of 30. Assuming there is no air resistance, what is the initial kinetic energy of the athlete.
The range of projectile is
L = v^2•sin2α/g,
v^2 = L•g/sin2α,
KE = mv^2/2 =m• L•g/2•sin2α
To calculate the initial kinetic energy of the athlete, we need to know the initial velocity of the shot put. We can determine the initial velocity by using the given information about the distance and angle.
To find the initial velocity, we first need to break down the initial velocity into its horizontal and vertical components. The horizontal component of velocity remains constant throughout the projectile's motion, while the vertical component is affected by gravity.
Using the angle of projection, which is given as 30 degrees, we can find the horizontal and vertical components of the velocity using trigonometric functions. The horizontal component of velocity (Vx) can be calculated using the formula:
Vx = initial velocity * cos(theta)
Where theta is the angle of projection.
The vertical component of velocity (Vy) can be calculated using the formula:
Vy = initial velocity * sin(theta)
Since there is no mention of time, we will assume that the shot put is launched and lands at the same height. This means that the vertical displacement (Δy) is zero.
Using the formula for vertical displacement (Δy) in projectile motion:
Δy = Vy * t + (1/2) * acceleration * t^2
Since Δy is zero, we can ignore the first term:
0 = (1/2) * acceleration * t^2
As there is no vertical acceleration (assuming no air resistance), the equation simplifies to:
0 = (1/2) * g * t^2
This implies that either time (t) is zero (which we can discard) or t^2 is zero. Since time cannot be zero, t^2 has to be zero.
t^2 = 0
Taking the square root of both sides gives us:
t = 0
This implies that the total flight time is zero, indicating that the shot put instantly reaches its maximum height and then lands back at the same height.
Now, let's go back and focus on the horizontal component of velocity (Vx). We know the horizontal displacement (Δx) is given as 24m. Using the formula for displacement in projectile motion:
Δx = Vx * t
Since t is zero, the equation simplifies to:
Δx = Vx * 0
This implies that the horizontal displacement (Δx) is also zero. However, we know that the shot put traveled a distance of 24m horizontally, so there must be an error in the given information.
Without the correct value for the horizontal displacement, we cannot calculate the initial velocity, and therefore, we cannot determine the initial kinetic energy of the athlete. It is essential to have accurate and complete information to solve the problem correctly.