YouIn a demonstration of skill, an archer shoots an apple which their assistant has thrown intothe air. The apple is thrown straight upwards and is still rising at 2.5 m/s when the arrowhits it. The arrow is travelling at 18 m/s at a 45 degree angle to horizontal the instant before itskewers the apple. The arrow has a mass of 20 g and the apple a mass of 180 g.(a) Determine the initial momentum of the combined apple-arrow system immediately before the arrow hits.

To solve this problem, we first need to understand the concept of momentum. Momentum is the product of an object's mass and its velocity. It's a vector quantity, which means it has both magnitude and direction.

(a) To determine the initial momentum of the combined apple-arrow system immediately before the arrow hits, we need to calculate the momentum of both the apple and the arrow separately and then add them together.

Step 1: Calculate the momentum of the apple. The apple's momentum (P_apple) can be calculated using the formula P = mv, where m is the mass and v is the velocity. The mass of the apple (m_apple) is 180g or 0.18kg (since 1kg = 1000g), and the velocity of the apple (v_apple) is 2.5m/s upwards. So,

P_apple = m_apple * v_apple = 0.18kg * 2.5m/s = 0.45 kg*m/s upwards

Step 2: Calculate the momentum of the arrow. The arrow's momentum (P_arrow) can also be calculated using the formula P = mv. The mass of the arrow (m_arrow) is 20g or 0.02kg, and the velocity of the arrow (v_arrow) is 18m/s at a 45 degree angle to the horizontal. However, since the apple is moving upwards, we are only interested in the vertical component of the arrow's velocity. We can find this by multiplying the arrow's speed by the sine of the angle (since sin(45) = 0.7071). So,

v_arrow_vertical = v_arrow * sin(45) = 18m/s * 0.7071 = 12.7272 m/s

Then,

P_arrow = m_arrow * v_arrow_vertical = 0.02kg * 12.7272m/s = 0.254544 kg*m/s upwards

Step 3: Add the momentum of the apple and the arrow. The total initial momentum (P_total) of the system is the sum of the momentum of the apple and the arrow. So,

P_total = P_apple + P_arrow = 0.45 kgm/s + 0.254544 kgm/s = 0.704544 kg*m/s upwards

So, the initial momentum of the combined apple-arrow system immediately before the arrow hits is 0.704544 kg*m/s upwards.