**Problem Statement:**A ball is thrown upward from a height of 112 feet above the ground, with an initial velocity of 96 feet per second. From physics, it is known that the velocity at time \( t \) is \( v(t) = 96 - 32t \) feet per second.**Questions:**a) Find \( s(t) \), the function giving the height of the ball at time \( t \).b) How long will the ball take to reach the ground?c) How high will the ball go?**Answer Template:**a) \( s(t) = \) [ ]b) The ball will reach the ground after [ ] seconds.c) The ball will go [ ] feet high.

(a) The position function of a ball can be given as, st=s0+∫0tvtdt=112+∫0t96-32tdt=112+96t-16t20t=112+96t-16t2(b) When a ball reaches the ground, the distance will be zero. s=0112+96t-16t2=0t=-1,7 The time can not be a negative value, so it can be negligible. The time taken by a ball to reach the ground is, t=7 s(c) At the maximum height, the velocity of a ball will be equal to zero. v=096-32t=0t=3 s The height of a ball is, s3=112+963-1632=256 ft

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Physics

A ball is thrown upward from a height of 112 feet above the ground, with an initial velocity of 96 feet per second. From physics it is known that the velocity at time t is v(t) = 96 - 32t feet per second. a) Find s(t), the function giving the height of the ball at time t. b) How long will the ball take to reach the ground? c) How high will the ball go? a) s(t) = b) The ball will reach the ground after seconds. c) The ball will go feet high.

A ball is thrown upward from a height of 112 feet above the ground, with an initial velocity of 96 feet per second. From physics it is known that the velocity at time t is v(t) = 96 - 32t feet per second. a) Find s(t), the function giving the height of the ball at time t. b) How long will the ball take to reach the ground? c) How high will the ball go? a) s(t) = b) The ball will reach the ground after seconds. c) The ball will go feet high.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Distance and Speed

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Question

**Problem Statement:**

A ball is thrown upward from a height of 112 feet above the ground, with an initial velocity of 96 feet per second. From physics, it is known that the velocity at time \( t \) is \( v(t) = 96 - 32t \) feet per second.

**Questions:**

a) Find \( s(t) \), the function giving the height of the ball at time \( t \).

b) How long will the ball take to reach the ground?

c) How high will the ball go?

**Answer Template:**

a) \( s(t) = \) [ ]

b) The ball will reach the ground after [ ] seconds.

c) The ball will go [ ] feet high.

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