Question

`DIRECTIONS: Write an answer to each question legible, using complete sentences and your own words as much as possible.

6.           What information is needed to directly determine the range of a projectile without using the equations of uniformly accelerated motion?

7.           At what point in its motion does an ideal projectile stop accelerating?

8.           Do two projectiles launched at complementary angles always yield the same range? Explain.

9.           When someone says that all measurement of motion is relative, what is it relative to? Give an example.

10.        Real projectiles do not have a maximum range for a 45^o launch. Discuss why the ideal angle for real projectiles (like baseballs, golf balls,..) is slightly lower than 45^o.

Answer 1

6)

The range of a projectile can be found out if the velocity of projection and the angle at which it is projected is given by the relation:

To help you understand the equation, let us try to derive it by considering a projectile which is projected with a velocity 'v' and an angle . Now, the range of the projectile is the horizontal component of the intial velocity of the projectile (which remains constant throughtout the motion of the projectile) multiplied by the time of flight of the projectile, i.e,

As we know that the only force that is acting on the projectile is the gravitation force, we can apply the equaiton of motion under constant acceleration to the vertical component of the motion of the projectile to find the time of flight by

Now, substituting the values in the first equation we get,

7)

For a projectile motion which does not go very high, there always a constant acceleration due to gravity acting on it without variation. Therefore, there are no such cases where the acceleration is zero in projectiles achieving less height. But if we consider the variation of g with altitude, the acceleration decreases as the projecitle moves higher.

8)

Yes, two projectiles launched with same velocity and at complimentary angles have same range. We can prove this by considering the first equation (in question part number 6) and two projectiles projected at velocity v and at angles and respectively. For the first case:

and for the second case:

Range

Hence both the projectiles have same range.

9)

When we say that motion of an object is relative, we mean that the motion is observed from a fixed frame of reference. This frame of reference may not stationary but can itself be in motion. For example, let us consider two cars on a highway. For a person standing on ground the speed of the cars is which the speedometer indicates, say, 60 and 70 mph respectively, Therefore, the speed of the cars relative to man, who is stationary, will be 60 and 70 mph. For a man sitting in the car moving with 60 mph, observes the car moving with 70mph and will notice that the car is approaching at10 mph (which is speed with respect his frame of reference) (70-60). Therefore, relative to the man sitting in car moving with 60 mph will take the speeds of two cars to be 0 and 10 mph respectively.

10)

The ideal angle is around . This is because in real condition there are factors such as air resistance acting on the object. Therefore, we need the object to cover maximum distance before it completely slows down.