# Linear Motion and Free Fall: Solving Projectile Motion Problems

• SuperNewb
In summary, the problem involves a mass being thrown straight up with an initial speed of 3.50 m/s from a height of 2.50 m, neglecting drag force. The acceleration of the object while moving up is -9.81m/s^2 and at the highest point it is 0. The maximum height that the mass reaches, the speed just before it hits the ground, and the speed at the highest point are all unknown as the relevant equations were not provided. However, the total time the object is in the air if it is allowed to freely fall to the ground can be calculated using the SUVAT equations. It is suggested to refer to the provided links for relevant equations and further assistance.
SuperNewb
Member advised to use the formatting template for questions posted to the homework forums
I. Free Fall Motion

A mass m = 544 g is thrown straight up with an initial speed of 3.50 m/s from a height of h = 2.50 m Neglecting a drag force,
determine:

1. The acceleration of the object while it moves up.
2. The acceleration of the object at the highest point.
3. The maximum height that the mass reaches.
4. The total time the object is in the air if it is allowed to freely fall to the ground.
5. The speed the mass has just before it hits the ground.
6. The speed of the mass at the highest point.
7. The speed of the mass at h = 2.50 m on its return trip down.

My prof. was very vague on our equations to use

from what I understand I was able to get

1. Acceleration while moving up = -9.81m/s^2
2. Acceleration = 0
3.
4. .357s
5.
6.
7.

feel free to suggest relevant equations for these problems.

Hello Newb,

The equations you need are called the SUVAT equations, in particular these. Doc Al has summarized them here

SuperNewb
What type of equations have you learned? Nothing in your textbook?

ProfuselyQuarky said:
What type of equations have you learned? Nothing in your textbook?

My professor didn't want us to use the book, and lectured on the philosophy of physics problem solving, but he never reviewed a problem involving a projectile moving up and then down

SuperNewb said:
My professor didn't want us to use the book, and lectured on the philosophy of physics problem solving, but he never reviewed a problem involving a projectile moving up and then down
That’s horrible . . . do BvU’s links help?

## 1. What is linear motion?

Linear motion, also known as rectilinear motion, is the motion of an object in a straight line with constant velocity.

## 2. What is free fall?

Free fall is the motion of an object under the influence of gravity, with no other external forces acting on it. In free fall, the object's acceleration is solely due to gravity and is approximately 9.8 m/s^2 near the Earth's surface.

## 3. How does air resistance affect linear motion and free fall?

Air resistance, or drag, can significantly affect the motion of an object in free fall. It acts in the opposite direction of the object's motion and increases as the object's velocity increases. This can cause the object to reach a terminal velocity, where the drag force is equal to the object's weight and the object stops accelerating.

## 4. What is the relationship between displacement, velocity, and acceleration in linear motion?

In linear motion, displacement (change in position) is directly proportional to velocity (change in position over time) and acceleration (change in velocity over time). This relationship is described by the equation: displacement = initial velocity * time + 1/2 * acceleration * time^2.

## 5. How is free fall different on other planets?

Free fall on other planets is affected by the planet's mass and radius, which determines the strength of its gravitational pull. This can result in different values for the acceleration due to gravity and therefore, different rates of free fall. For example, on the moon, the acceleration due to gravity is 1.62 m/s^2, compared to 9.8 m/s^2 on Earth.

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