A ball is thrown straight up in the air leaving your hand 1 m from the ground, w

Question

A ball is thrown straight up in the air leaving your hand 1 m from the ground, with an initial velocity of 8 m/s. 6. Choose a coordinate system for this problem. a. b. Is this a constant acceleration problem. c. Find the time it takes to reach the maximum height. d. Find the maximum height obtained by the ball. e. Find the time to reach the ground. f. Find the velocity when the ball hits the ground 7. A ball is thrown at 25 m/s at an angle of 25 above the horizontal. Choose a coordinate system and sketch the motion of the ball. a. b. Find the initial velocity of the ball in the x and y directions. c. Find when the ball reaches its highest point.

Explanation / Answer

6.(a)

Choose a coordinate system (x-y) showing upward motion Pf ball at 1 m from ground. You can choose ground as origin.

(b)

Yes, This is a constant acceleration problem. The acceleration is acceleration due to gravity only , which is in vertically downward direction. Also at maximum height , its velocity becomes zero but acceleration won't be changed.

(C). Applying equation of motion :

V = u+at

V= 0 , at maximum height

u= 8 m/s ( given )

a = -9.81 m/s2

0 = 8 - (9.81)t

t = 0.82 s

(D)

By equation :

r = r0+v0t + (1/2)at2

r = 1 + (8)(0.82)+(1/2)(-9.81)(0.82)2

r = 4.26 m from the ground

(E) by equation :

r = r0+v0t + (1/2)at2

0= 4.26 + 0+ (1/2)(-9.81)t2

t = 0.93 s

(F) velocity when ball hits ground

v2= v02+2a(r-r0)

v2= 0 + 2(-9.81)(0-4.26)

v = 9.14 m/s

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