How Do You Calculate Initial Velocity in Projectile Motion?

[killjoy2019]

Homework Statement

A ball is thrown downward from a tower 65.0 m tall. If the ball takes 1.30 seconds to hit the ground, what was its initial velocity?

The answer my teacher provides is 43.6 m/s, but I am having a problem reaching that answer.

Homework Equations

Possibly Vi = Vf - aT? This is the equation I am trying to use, but the final velocity is not given, I don't think.

The Attempt at a Solution

First, I tried Vi = 0 + 9.8 x 1.3, but obviously, it doesn't work. So whether there is information missing or I am using the wrong formula, I don't know. Any help would be appreciated!

 

[PeterO]

Homework Statement

A ball is thrown downward from a tower 65.0 m tall. If the ball takes 1.30 seconds to hit the ground, what was its initial velocity?

The answer my teacher provides is 43.6 m/s, but I am having a problem reaching that answer.

Homework Equations

Possibly Vi = Vf - aT? This is the equation I am trying to use, but the final velocity is not given, I don't think.

The Attempt at a Solution

First, I tried Vi = 0 + 9.8 x 1.3, but obviously, it doesn't work. So whether there is information missing or I am using the wrong formula, I don't know. Any help would be appreciated!

The values you have are:

x - displacement - 65
a - acceleration due to gravity - 9.8
t - time - 1.3

All motion and acceleration is down, so I have made all values positive

You want v_i

so you need the motion formula with out the final velocity. That is

x = v_i.t + 0.5.a.t²

sub values into that and see how you go.

 

[killjoy2019]

Thank you! That seem to have worked. (: I knew there was something wrong with the formula I was using.

 

[PeterO]

Thank you! That seem to have worked. (: I knew there was something wrong with the formula I was using.

You should always identify those values you know, and the value(s) you want, to help in deciding which formula to use.

 

[asteriatic]

I would like to clarify that there are two types of motion being discussed here - linear motion and projectile motion. Linear motion refers to the motion of an object in a straight line, while projectile motion refers to the motion of an object that is projected into the air and follows a curved path due to the influence of gravity.

In this problem, we are dealing with projectile motion as the ball is thrown downward from a tower. To solve for the initial velocity, we can use the equation Vf = Vi + at, where Vf is the final velocity, Vi is the initial velocity, a is the acceleration due to gravity (9.8 m/s^2), and t is the time (1.30 seconds).

Since the ball is thrown downward, the initial velocity will be negative. Therefore, we can rewrite the equation as -Vf = Vi - at. Plugging in the given values, we get:

-Vf = Vi - (9.8 m/s^2)(1.30 s)
-Vf = Vi - 12.74 m/s

We also know that the final velocity when the ball hits the ground will be 0 m/s. Therefore, we can rewrite the equation as 0 = Vi - 12.74 m/s and solve for Vi:

Vi = 12.74 m/s

However, this is the magnitude of the initial velocity. Since the initial velocity is negative, we can write it as -12.74 m/s. But since the ball is thrown downward, the magnitude is more important in this case, so the answer would be 12.74 m/s.

It is possible that your teacher used a different approach or formula to solve for the initial velocity. But as long as you understand the concepts of projectile motion and how to use the appropriate equations, you should be able to arrive at the correct answer. I hope this helps!