An object is shot vertically upward from the ground with an initial velocity of 224 ft/sec. For vertical motion near the Earth's surface, acceleration due to gravity is -32 feet per second squared. (The negative means that acceleration is downward.) (a) Explain why the graph of velocity of the object against time is linear. O The graph of velocity is linear because the acceleration is decreasing at a constant rate. O The graph of velocity is linear because the velocity is increasing at a constant rate. O The graph of velocity is linear because the velocity is decreasing at a constant rate. O The graph of velocity is linear because the velocity is constant. O The graph of velocity is linear because the acceleration is increasing at a constant rate. (b) Using the starting velocity and your answer to part (b), find the time at which the object reaches the highest point. sec (c) Use your answer to part (c) to decide when the object hits the ground. sec (d) Graph the velocity against time. Mark on the graph when the object reaches its highest point and when it lands. v(t) v(t) 224 224 O-224 v(t) 224 0-224 Highest point Highest point t Lands Lands O-224 Highest point v(t) 224 O-224 (e) Find the maximum height reached by the object by considering an area on a graph. ft Highest point t Lands Lands

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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An object is shot vertically upward from the ground with an initial velocity of 224 ft/sec. For vertical motion near the Earth's surface, acceleration due to gravity is -32 feet per second squared. (The negative means that acceleration is downward.)
(a) Explain why the graph of velocity of the object against time is linear.
O The graph of velocity is linear because the acceleration is decreasing at a constant rate.
O The graph of velocity is linear because the velocity is increasing at a constant rate.
O The graph of velocity is linear because the velocity is decreasing at a constant rate.
The graph of velocity is linear because the velocity is constant.
The graph of velocity is linear because the acceleration is increasing at a constant rate.
(b) Using the starting velocity and your answer to part (b), find the time at which the object reaches the highest point.
sec
(c) Use your answer to part (c) to decide when the object hits the ground.
sec
(d) Graph the velocity against time. Mark on the graph when the object reaches its highest point and when it lands.
v(t)
224
v(t)
224
-224
v(t)
224
-224
Highest point
Highest point
t
Lands
t
Lands
-224
v(t)
224
Highest point
-224
(e) Find the maximum height reached by the object by considering an area on a graph.
ft
Highest point
t
Lands
t
Lands
Transcribed Image Text:An object is shot vertically upward from the ground with an initial velocity of 224 ft/sec. For vertical motion near the Earth's surface, acceleration due to gravity is -32 feet per second squared. (The negative means that acceleration is downward.) (a) Explain why the graph of velocity of the object against time is linear. O The graph of velocity is linear because the acceleration is decreasing at a constant rate. O The graph of velocity is linear because the velocity is increasing at a constant rate. O The graph of velocity is linear because the velocity is decreasing at a constant rate. The graph of velocity is linear because the velocity is constant. The graph of velocity is linear because the acceleration is increasing at a constant rate. (b) Using the starting velocity and your answer to part (b), find the time at which the object reaches the highest point. sec (c) Use your answer to part (c) to decide when the object hits the ground. sec (d) Graph the velocity against time. Mark on the graph when the object reaches its highest point and when it lands. v(t) 224 v(t) 224 -224 v(t) 224 -224 Highest point Highest point t Lands t Lands -224 v(t) 224 Highest point -224 (e) Find the maximum height reached by the object by considering an area on a graph. ft Highest point t Lands t Lands
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