Question

A baseball is thrown from the roof of h = 23.4-m -tall building with an initial velocity of magnitude 11.0 m/s and directed at an angle of 53.1 ∘ above the horizontal. what is the speed of the ball just before it strikes the ground? use energy methods and ignore air resistance. what is the answer for part (a) if the initial velocity is at an angle of 53.1 ∘ below the horizontal? if the effects of air resistance are included, will part (a) or (b) give the higher speed?

Answer 1

Using energy conservation methods, we can calculate the final speed of a baseball thrown from a building by equating the potential and kinetic energy at the top to the kinetic energy just before impact. The same calculation applies whether the ball is thrown upwards or downwards if air resistance is ignored. However, with air resistance, the ball thrown downwards would likely have a higher speed upon impact.

Step-by-step explanation:

To find the speed of the baseball just before it strikes the ground when thrown from a 23.4-meter-tall building with an initial velocity of 11.0 m/s at a 53.1-degree angle above the horizontal, we can use energy methods. The mechanical energy at the start (potential plus kinetic) will equal the kinetic energy just before impact because air resistance is ignored. Since the potential energy at the top is converted to kinetic energy at the bottom, we calculate:

PEtop + KEtop = KEbottom

mgh + (1/2)mv2 = (1/2)mv'2

Solving for v' gives you the speed just before impact. If the ball is thrown at the same angle below the horizontal, the speed before impact would be the same due to symmetry and ignoring air resistance.

When considering air resistance, the speed before impact will be less than without air resistance for both scenarios. However, the ball thrown downwards would likely have a higher speed upon impact compared to the one thrown upwards, since it has a shorter distance to travel and thus less time for air resistance to act on it.