Projectile Motion Problems

Category: Mechanics, Physics

"Published in Newark, California, USA"

An object falls from a plane flying horizontally at an altitude of 40,000 ft. at 500 mi/hr. How long will it take to hit the ground? What is the horizontal distance traveled of an object?

Solution:

The given problem is about projectile motion in which an object is thrown from its maximum height with an initial velocity. The projectile curve is a half-parabola as shown in the figure below

Photo by Math Principles in Everyday Life

First, let's consider the y-component of an object in order to calculate the time required to hit the ground. From the distance formula
 

Since an object is thrown in a downward position, then the values of s_y and a_y are negative. a_y is also equal to g = 32.174 ft/sec²  which is an acceleration due to gravity. V_0y is zero because the direction of initial velocity of an object is horizontal. Therefore, the time required of an object to hit the ground is
 

          

 

 

 

 

Next, let's consider the x-component of an object in order to calculate the horizontal distance traveled of an object. From the distance formula

Since the direction of v_0x is horizontal and constant, then a_x is equal to zero. Therefore, the horizontal distance traveled of an object is

                      or

Rate, Distance, and Time Problems, 8

Category: Physics, Mechanics

"Published in Newark, California, USA"

A runner A can run the mile race in 4.25 min. Another runner B requires 4.55 min to run this distance. If they start out together and maintain their normal speeds, how far apart will they be at the finish of the race?

Solution:

The given problem is about rate, distance, and time problem in which the two runners run in the same mile race. From the given problem also, runner A is faster than runner B because runner A has a lesser time to complete the mile race than runner B.

The speed of runner A is

The speed of runner B is

If the two runners will start together in a mile race, then runner A will finish the race. Therefore, their distance between the two runners at the end of the race is

For runner B, we use the time for runner A because runner A will finish the race.

                        or

 

Rate, Distance, and Time Problems, 7

Category: Physics, Mechanics

"Published in Newark, California, USA"

A motorist has to travel 3.50 km in a city where his average speed should not exceed 25 km/hr. If he increases his average speed to 40 km/hr, how much time will he gain in his journey?

Solution:

The given problem is about rate, distance, and time problem in which the average speed is increased. Let's assume that the distance for the two cases is the same which is 3.50 km. 

If the speed limit in a city is 25 km/hr, then his travel time is

If he increased his speed to 40 km/hr, then his travel time is
 

 

 

 

Therefore, his travel time will gain by
 

 

 

                         or