A body is thrown with a velocity `v_0` at an angle `theta_0` with horizontal. Find the (a) instantaneous power delivered by gravity after a time t measured from the instant of projection and (b) average power delivered by gravity during the time t.

Explanation

To solve the problem step by step, we will address both parts: (a) the instantaneous power delivered by gravity after a time \( t \) and (b) the average power delivered by gravity during the time \( t \).

### Step-by-Step Solution

**Part (a): Instantaneous Power Delivered by Gravity**

1. **Identify the Components of Initial Velocity:**
The body is thrown with an initial velocity \( v_0 \) at an angle \( \theta_0 \). The components of the initial velocity can be expressed as:
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