Homework 20 You must show all work to receive credit. Write in a clear and organ

Question

Homework 20 You must show all work to receive credit. Write in a clear and organized manner; u 1 Warm-up Questions Att - 0, a football is kicked with an initial velocity of 25.0 m/s at an angle O 15° above the horizontal. ndlear work will not receive credit. This ball undergoes projectile motion where air resistance is negligible. It's usually simplest to take the vertie e o) as the origin, as shown on the picture, with the typical hice ( horizontal. of coordinates. a) What is the z-component of the ball's initial velocity vector: b) What is the y-component of the ball's initial velocity vector: c) What is the direction of the acceleration of the ball (after it is in the air): d) What is the r-component of the acceleration vector e) What is the y-component of the acceleration vector ) Express the projectile's position Fl), velocity (), and acceleration ate) by separate equations for the horizontal and vertical components in terms of the variable t (hint-which ones are constant? ones are 02): r(t)- y(t) ay(t)

Explanation / Answer

a) A projectile is one in which a body is projected in air with some angle other than 90degrees

Given the initial velocity of the ball is u = 25 m/s . The ball is projected at angle of 15o

The horizontal component of the initial velocity is ux = u cos 15o = 25 Cos 15o

b) The Vertical component of the initial velocity is uy = u Sin 15o = 25 Sin 15o

c) As the body is in projectile motion, the acceleration is nothing but the acceleration due to gravity therefore the dierction is always vertically downwards.

d) As the accelertion acts vertically downwards, the angle is 90o hence, the horizontal component of acceleration is g Cos90o = 0

e) The vertical component of aceleration is g Sin 90o = g = 9.8 m/s2

f) We know the equations of motion,

For position the equation is, r(t) = ut + (1/2) at2

the horizontal component of position is x = (uCos 15o)t, as the horizontal component of acceleration is zero,

the vertical component of position is x = (u Sin 15o)t - (1/2) gt2, as the vertical component of acceleration is 'g' and the body is moving upwards.

For velocity, the equation is v = u + at

The horizontal component of velocity is vx = uCos 15o = 25Cos 15o (horizontal component of acceleration is zero)

The vertical component of velocity is vy = u Sin15o - gt= 25Sin 15o - 9.8t

The Horizontal component of acceleration is zero and the vertical component is 'g'. 'g' is always constant

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