# Projectile: time max height reached

• Newlander
In summary, the conversation discusses the calculation of the time it takes for a boy's thrown rock to reach its maximum height. The initial velocity of the rock is given as 3.13 m/s at an angle of 30 degrees above the horizontal. After attempting to use the formula vf=vi+at, the poster becomes concerned about a potential typo in the given answer of 0.313 seconds. The expert responds by suggesting to apply the formula to the vertical velocity component and taking into account the more precise measurement of -10 m/s^2 for acceleration due to gravity, resulting in a final answer of 0.319 seconds.
Newlander

## Homework Statement

"A boy throws a rock with an initial velocity of 3.13 m/s at 30.0 degrees above the horizontal. How long does it take for the rock to reach the maximum height of its trajectory?"

vi = 3.13 m/s
tmax height = ?
vf = 0 m/s (at max height)
a = -9.8 m/s2

vf = vi + at

(Not sure!)

## The Attempt at a Solution

vf = vi + at
t = [(vf - vi) / a] = [(0 m/s - 3.13 m/s)/-9.8 m/s2]
t = 0.319 s

Concern:
The correct answer is listed as 0.313 s; because my answer is so close, I wondered if this were a typo. If not, I clearly am taking the wrong approach and would appreciate some guidance.

The ball has been thrown at an angle, and the magnitude of the initial velocity is 3.13 m/s. With what initial velocity does the ball move upward?

ehild

Hmmm . . . so, I should determine viy? If so, 3.13 m/s sin(30) = 1.57 m/s . . . sorry--not clear on how this will help me arrive at what's noted as the correct answer. I did plug this figure into vf2 - vi2 = 2ad, and then determined d from that . . . and then plugged that d into d = vit + 1/2at2 to determine t . . . but I ended up with the same answer, 0.319 s.

You have the formula vf=vi+at already. Apply it to the vertical velocity components. At the maximum height, vy=0 (not the velocity v, as the ball keeps it horizontal velocity component during the whole flight)

ehild

Lol, this is going to seem so simple after . . .

You used: -9.8m/s2

They used: -10m/s2

You got the correct answer under a more precise measurement.

Last edited:

## 1. What is the equation for calculating the time at which a projectile reaches its maximum height?

The equation for calculating the time at which a projectile reaches its maximum height is t = vy/g, where t is the time in seconds, vy is the vertical component of the velocity in meters per second, and g is the acceleration due to gravity in meters per second squared.

## 2. How does the mass of a projectile affect the time it takes to reach its maximum height?

The mass of a projectile does not affect the time it takes to reach its maximum height. This is because the acceleration due to gravity is independent of the mass of an object. However, a heavier projectile will have a greater weight and therefore experience a greater force due to gravity, resulting in a higher maximum height reached.

## 3. Can a projectile ever reach its maximum height at more than one point during its trajectory?

No, a projectile can only reach its maximum height once during its trajectory. This is because the maximum height reached is the point at which the vertical component of the velocity becomes zero, after which the projectile begins to fall back down due to the force of gravity.

## 4. How does air resistance affect the time at which a projectile reaches its maximum height?

Air resistance, also known as drag, can affect the time at which a projectile reaches its maximum height by slowing down the projectile's upward velocity. This means that it will take longer for the projectile to reach its maximum height compared to if there was no air resistance present.

## 5. Is there a way to increase the time it takes for a projectile to reach its maximum height?

Yes, there are a few ways to increase the time it takes for a projectile to reach its maximum height. One way is to increase the initial velocity of the projectile, either by increasing the launch angle or the magnitude of the velocity. Another way is to decrease the acceleration due to gravity, which can be achieved by launching the projectile on a planet with a lower gravitational pull. Additionally, reducing the effects of air resistance can also increase the time it takes for a projectile to reach its maximum height.

• Introductory Physics Homework Help
Replies
2
Views
3K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
2K
• Introductory Physics Homework Help
Replies
15
Views
4K
• Introductory Physics Homework Help
Replies
9
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
827