Use the equations below:

P=mv
Ek=1/2mv^2
4) A wooden target of mass 2.00kg is suspended from a branch so that it swings freely. The target is hit by an arrow of mass 0.10kg travelling horizontally and the arrow embeds itself in the centre of the target. The target swings upwards, with its centre of mass rising by 0.60m. Use 9.81 as the acceleration for gravity.

A) Calculate the gain in gravitational energy by the target and arrow combination.
B) Calculate the velocity of the arrow and target immediately after the impact.
C) Calculate the velocity of the arrow immediately before the impact.
D) Determine if the collision is elastic or inelastic and why.
12 marks

please answer

i needed this answered a long time ago cmon

To solve this problem, we can use the principles of conservation of energy, momentum, and the equations given.

A) To calculate the gain in gravitational energy by the target and arrow combination, we need to determine the change in height.

Change in gravitational potential energy (ΔPE) = mgh

Here, mass (m) is the combined mass of the target and arrow, which is the sum of their individual masses, with values of 2.00 kg and 0.10 kg, respectively. The acceleration due to gravity (g) is given as 9.81 m/s², and the change in height (h) is 0.60 m.

ΔPE = (2.00 kg + 0.10 kg) * 9.81 m/s² * 0.60 m

Calculate the result to find the gain in gravitational energy.

B) To determine the velocity of the arrow and target immediately after the impact, we can use the principle of conservation of momentum.

Conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.

Initial momentum (P_initial) = Final momentum (P_final)

The initial momentum is the product of the mass (m) and the initial velocity of the arrow (v1), which we want to find.

The final momentum is the product of the combined mass (m) and the final velocity (v2) of the arrow and the target, which we want to calculate.

P_initial = P_final

(m1 * v1) = (m1 + m2) * v2

Substitute the given values of masses and solve for v2.

C) To calculate the velocity of the arrow immediately before the impact, we can use the equation given: P = mv

We are given the mass (m) of the arrow (0.10 kg) and the final velocity (v2) after the impact. Rearrange the equation to solve for v1.

v1 = P_initial/m1

Substitute the values of P_initial and m1.

D) To determine if the collision is elastic or inelastic, we need to compare the kinetic energy before and after the collision.

If the kinetic energy remains the same before and after the collision, it is an elastic collision.

If the kinetic energy decreases after the collision, it is an inelastic collision.

Calculate the kinetic energy before and after the collision using the equation given: Ek = 1/2mv²

If the kinetic energy is conserved, it is an elastic collision. If not, it is an inelastic collision.

Now you have all the steps to solve the problem. Plug in the values provided and perform the calculations to find the answers.