A baseball is thrown from the rood of a 27.5m tall building with an initial velocity of magnitude 16.0m/s and directed at an angle of 37 degrees above the horizontal.

A) Using energy methods and ignoring air resistance, calculate the speed of the ball just before it strikes the ground.

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To calculate the speed of the ball just before it strikes the ground using energy methods, we need to consider the potential energy and kinetic energy of the ball at different points.

We can start by calculating the potential energy of the ball when it is at the roof of the building. The potential energy (PE) is given by the equation:

PE = mgh

Where m is the mass of the ball, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height of the building.

Given: h = 27.5 m

Next, we need to calculate the kinetic energy of the ball just before it strikes the ground. The kinetic energy (KE) is given by the equation:

KE = 0.5 * mv^2

Where m is the mass of the ball and v is its velocity.

To apply energy conservation, we assume no energy losses due to air resistance. Therefore, the potential energy at the top of the building is equal to the kinetic energy just before the ball hits the ground:

mgh = 0.5 * mv^2

We can cancel out the mass (m) from both sides of the equation:

gh = 0.5 * v^2

Now, we can solve for v, the speed of the ball just before it strikes the ground:

v^2 = 2gh

v = √(2gh)

We substitute the known values:

v = √(2 * 9.8 m/s^2 * 27.5 m)

Calculating this expression will give us the speed of the ball just before it strikes the ground.