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1. A parkour enthusiast attempts a dangerous jump from building to building, which involves a drop of 4.05 m from rooftop to rooftop across a gap of 5.20 m. He can run at a maximum speed of 5.80 m/s.

a) Show that he can safely make the jump. (Assume that his initial velocity is horizontal. b) How fast is he moving just before he lands?

**Problem Statement**

1. A parkour enthusiast attempts a dangerous jump from building to building, which involves a drop of 4.05 m from rooftop to rooftop across a gap of 5.20 m. He can run at a maximum speed of 5.80 m/s.

(a) Show that he can safely make the jump. (Assume that his initial velocity is horizontal.)

(b) How fast is he moving just before he lands?

**Explanation**

- **Part (a):** To determine if the parkour enthusiast can safely make the jump, calculate the time it takes to fall 4.05 m. Use the formula for vertical motion under gravity:

\[
y = \frac{1}{2} g t^2
\]

Where \( y = 4.05 \, \text{m} \) and \( g = 9.81 \, \text{m/s}^2 \). Calculate \( t \) and then determine if the horizontal distance covered in this time at 5.80 m/s is at least 5.20 m.

- **Part (b):** Determine the speed just before landing by calculating both the horizontal and vertical velocity components before landing, and use the Pythagorean theorem to find the resultant velocity.

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