Projectile Motion Tutorial Learning Goal: To understand how to apply the equatio

Question

Projectile Motion Tutorial

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 v 0 . In this problem we are assuming that the ground is level.

Part A

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

Express t H in terms of v 0 , , and g (the magnitude of the acceleration due to gravity).

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Part B

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

Express the time in terms of v 0 , , and g .

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Part C

Find H , the maximum height attained by the projectile.

Express your answer in terms of v 0 , , 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 v 0 , , and g .

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Figure 1 of 1

Projectile Motion Tutorial

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 v 0 . In this problem we are assuming that the ground is level.

Part A

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

Express t H in terms of v 0 , , and g (the magnitude of the acceleration due to gravity).

SubmitHintsMy AnswersGive UpReview Part

Part B

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

Express the time in terms of v 0 , , and g .

SubmitHintsMy AnswersGive UpReview Part

Part C

Find H , the maximum height attained by the projectile.

Express your answer in terms of v 0 , , and g .

SubmitHintsMy AnswersGive UpReview Part

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 v 0 , , and g .

SubmitHintsMy AnswersGive UpReview Part

Provide FeedbackContinue

R =

Figure 1 of 1

H = t R = t H =

Explanation / Answer

here,

A)

the time taken for the maximum height , th = v0*sin(theta)/g

B)

as it taken twice the time to reach the maximum height to cover distance R

the time at which projectile hits the ground , t = 2 *v0 * sin(theta)/g

(C)

using third equation of motion

0 - (v0 * sin(theta))^2 = - 2 * g* Hmax

Hmax = (v0 * sin(theta))^2 /2g

the maximum height is
Hmax = (v0 * sin(theta))^2 /2g

(D)

the total distance R = v*cos(theta) * t

R = v*cos(theta) * 2 *v0 * sin(theta)/g

R = v^2 * sin(2*theta) /g

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