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Solving problems is an essential part of the understanding process.

Questions and their answers are presented here in the module text format as if it were an extension of the treatment of the topic. The idea is to provide a verbose explanation, detailing the application of theory. Solution presented is, therefore, treated as the part of the understanding process – not merely a Q/A session. The emphasis is to enforce ideas and concepts, which can not be completely absorbed unless they are put to real time situation.

Hints on solving problems

1: In general, we should rely on analysis in two individual directions as linear motion.

2: Wherever possible, we should use the formula directly as available for time of flight, maximum height and horizontal range.

3: We should be aware that time of flight and maximum height are two attributes of projectile motion, which are obtained by analyzing motion in vertical direction. For determining time of flight, the vertical displacement is zero; whereas for determining maximum height, vertical component of velocity is zero.

4: However, if problem has information about motion in horizontal direction, then it is always advantageous to analyze motion in horizontal direction. It is so because motion in horizontal direction is uniform motion and analysis in this direction is simpler.

5: The situation, involving quadratic equations, may have three possibilities : (i) quadratic in time "t" (ii) quadratic in displacement or position "x" and (iii) quadratic in "tanθ" i.e."θ". We should use appropriate equations in each case as discussed in the module titled " Features of projectile motion ".

Representative problems and their solutions

We discuss problems, which highlight certain aspects of the study leading to the features of projectile motion. The questions are categorized in terms of the characterizing features of the subject matter :

  • Time of flight
  • Horizontal range
  • Maximum height
  • Height attained by a projectile
  • Composition of motion
  • Projectile motion with wind/drag force

Time of flight

Problem : The speed of a particle, projected at 60°, is 20 m/s at the time of projection. Find the time interval for projectile to loose half its initial speed.

Solution : Here, we see that final and initial speeds (not velocity) are subject to given condition. We need to use the given condition with appropriate expressions of speeds for two instants.

u = u x 2 + u y 2

v = v x 2 + v y 2

According to question,

u = 2 v

u 2 = 4 v 2

u x 2 + u y 2 = 4 v x 2 + v y 2

But, horizontal component of velocity remains same. Hence,

u x 2 + u y 2 = 4 u x 2 + v y 2

Rearranging for vertical velocity :

v y 2 = u y 2 - 3 u x 2 = 20 sin 60 0 2 - 3 X 20 cos 60 0 2

v y 2 = 20 X 3 4 - 3 X 20 X 1 4 = 0

The component of velocity in vertical direction becomes zero for the given condition. This means that the projectile has actually reached the maximum height for the given condition. The time to reach maximum height is half of the time of flight :

t = u sin θ g = 20 X sin 60 0 10 = 3 s

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Horizontal range

Problem : A man can throw a ball to a greatest height denoted by "h". Find the greatest horizontal distance that he can throw the ball (consider g = 10 m / s 2 ).

Solution : The first part of the question provides the information about the initial speed. We know that projectile achieves greatest height in vertical throw. Let "u" be the initial speed. We can, now, apply equation of motion " v 2 = u 2 + 2 g y " for vertical throw. We use this form of equation as we want to relate initial speed with the greatest height.

Here, v = 0; a = -g

0 = u 2 - 2 g h u 2 = 2 g h

The projectile, on the other hand, attains greatest horizontal distance for the angle of projection, θ = 45°. Accordingly, the greatest horizontal distance is :

R max = u 2 sin 2 X 45° g = u 2 sin 90° g = u 2 g = 2 g h g = 2 h

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Questions & Answers

List the application of projectile
Luther Reply
How can we take advantage of our knowledge about motion?
Kenneth Reply
pls explain what is dimension of 1in length and -1 in time ,what's is there difference between them
Mercy Reply
what are scalars
Abdhool Reply
show that 1w= 10^7ergs^-1
Lawrence Reply
what's lamin's theorems and it's mathematics representative
Yusuf Reply
if the wavelength is double,what is the frequency of the wave
Ekanem Reply
What are the system of units
Jonah Reply
A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
58asagravitasnal firce
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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