Learning Goal: To understand how to apply the equations for one-dimensional moti

Question

Learning Goal:

To understand how to apply the equations for one-dimensional motion to the x and y directions separately in order to derive standard formulas for the range and height of a projectile.

(Figure 1) A projectile is fired from ground level at time t=0 , at an angle with respect to the horizontal. It has an initial speed v0 . In this problem we are assuming that the ground is level.

Part A

Find the time tH it takes the projectile to reach its maximum height H .

Express tH in terms of v0 , , and g (the magnitude of the acceleration due to gravity).

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Part B

Find tR , the time at which the projectile hits the ground after having traveled through a horizontal distance R .

Express the time in terms of v0 , , and g .

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Part C

Find H , the maximum height attained by the projectile.

Express your answer in terms of v0 , , and g .

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Part D

Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.

Express the range in terms of v0 , , and g .

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Figure 1 of 1

Learning Goal:

To understand how to apply the equations for one-dimensional motion to the x and y directions separately in order to derive standard formulas for the range and height of a projectile.

(Figure 1) A projectile is fired from ground level at time t=0 , at an angle with respect to the horizontal. It has an initial speed v0 . In this problem we are assuming that the ground is level.

Part A

Find the time tH it takes the projectile to reach its maximum height H .

Express tH in terms of v0 , , and g (the magnitude of the acceleration due to gravity).

SubmitHintsMy AnswersGive UpReview Part

Part B

Find tR , the time at which the projectile hits the ground after having traveled through a horizontal distance R .

Express the time in terms of v0 , , and g .

tH =

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Part C

Find H , the maximum height attained by the projectile.

Express your answer in terms of v0 , , and g .

tR =

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Part D

Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.

Express the range in terms of v0 , , and g .

H =

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R =

Figure 1 of 1

Explanation / Answer

Part A

Find the time tH it takes the projectile to reach its maximum height H .

Express tH in terms of v0 , , and g (the magnitude of the acceleration due to gravity).

At maximum height H the vertical velocity is zero

V =vosin –gtH

tH = vosin/g

Part B

Find tR , the time at which the projectile hits the ground after having traveled through a horizontal distance R .

Express the time in terms of v0 , , and g .

Total vertical displacement S = H – H = 0

S = vosintf – ½ gtf2 = 0

tf =2vosin/g

Part C

Find H , the maximum height attained by the projectile.

Express your answer in terms of v0 , , and g

At maximum height H the vertical velocity is zero

V2 = vo2sin2 – 2gH

H = vo2sin2 / 2g

Part D

Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.

Express the range in terms of v0 , , and g .

The horizontal motion have no change in velocity

R = vocostf

= vo2(2cossin)/ g

= vo2sin2/g

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