A light shines from the top of a pole 40 ft high. A ball is dropped from the same height from a point 30 ft away from the light. How fast ball moving along the ground 1 sec later? (Assume the ball falls a distance s = 16t² in t sec.) The shadow is moving at a velocity of ft/sec. (Type an integer or a decimal.) the shadow of the 40-ft pole 0 30 Ball at time t-0 1 sec later Shadow x(1)
A light shines from the top of a pole 40 ft high. A ball is dropped from the same height from a point 30 ft away from the light. How fast ball moving along the ground 1 sec later? (Assume the ball falls a distance s = 16t² in t sec.) The shadow is moving at a velocity of ft/sec. (Type an integer or a decimal.) the shadow of the 40-ft pole 0 30 Ball at time t-0 1 sec later Shadow x(1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Shadow Velocity Problem
**Problem Statement:**
A light shines from the top of a pole 40 ft high. A ball is dropped from the same height from a point 30 ft away from the light. How fast is the shadow of the ball moving along the ground 1 second later? (Assume the ball falls a distance \( s = 16t^2 \) in \( t \) seconds.)
**Diagram Explanation:**
- The diagram to the right illustrates this scenario:
- A 40-ft pole is depicted with a light at the top.
- A ball is initially at the height of the pole and 30 ft away horizontally from the pole's base.
- After 1 second, the ball's position is lower due to gravity, and its shadow is projected further along the ground.
**Solution:**
- The shadow is moving at a velocity of \(\_\_\_\) ft/sec.
- (Type an integer or a decimal.)
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