Initial Velocity of Projectile Motion, given displacement and initial angle?

• allure
In summary: From what angle was the grasshopper initially at?From what angle was the grasshopper initially at, it was at 45.0°. So the x-component of its initial speed is 0.
allure

Homework Statement

A grasshopper jumps 1.00 meters from rest, with an initial velocity at a 45.0° angle with respect to the horizontal. Find (a) the initial speed of the grasshopper and (b) the maximum height reached.

Homework Equations

vx = v0xt = v0cos θ0

vy = v0 sin θ0 - gt

The Attempt at a Solution

I was unsure what to do, so I resolved for the components, resulting in

v0x = v0 cos 45°

v0y = v0 sin 45°

I apologize for my cluelessness - this my first semester in physics (at all), and I am having trouble finding where to go about this problem. Thank you in advance.

Last edited:
is that 1.00 supposed to be in meters? Is the grasshopper jumping 1.00 meter forward across the ground?

also, when the grasshopper reaches the peak of its arc through the air, what is the magnitude of the *vertical component* of the velocity? (this is a question that is trying to push you in the right path, the first one is clearing up some confusion on what the problem is asking)

Yes, meters - sorry. I have edited the above.

SHISHKABOB said:
is that 1.00 supposed to be in meters? Is the grasshopper jumping 1.00 meter forward across the ground?

also, when the grasshopper reaches the peak of its arc through the air, what is the magnitude of the *vertical component* of the velocity? (this is a question that is trying to push you in the right path, the first one is clearing up some confusion on what the problem is asking)

The velocity of the peak of the arc would be 0. I tried to look for a way to use this to find the initial speed but I'm stuck, is there a way I can use this information to do that?

well so you can solve for the t it takes to get to that point

and so then if that's the amount of time it takes to get to the *peak*, how long does it take the grasshopper to go the full distance?

So far, I've solved using Vy sin θ0 - gt
to get

tmax = v0sin 45°/9.8

ttotal = 2(v0 sin 45°/9.8)

Without the initial velocity, I'm not sure how (if I can) to simplify any further, or solve for it..

45 degrees is right in the middle of completely horizontal and completely vertical. You might feel like the horizontal and vertical components should be the same, and indeed they are. cos45=sin45 Might as well take Vox and call it Voy

X = Voyt ,where X is the horizontal distance traveled.

Vyf = Voy -gt

However Vyf is right before hitting the ground... it must have equal magnitude but opposite direction of Voy so:

-Vyo = Voy -gt

So you have 2 equations, two unknowns and can solve.

Last edited:
so if you know that the time taken for the grasshopper to end its jump is ttotal = 2(v0 sin 45°/9.8)

and that it went 1 meter

and you know that

x = v0,xt = v0cos(θ)t

what could you do with that

1. What is the formula for calculating the initial velocity of a projectile given its displacement and initial angle?

The formula for calculating the initial velocity of a projectile is v0 = √(d/g * tanθ), where v0 is the initial velocity, d is the displacement, g is the acceleration due to gravity, and θ is the initial angle.

2. How do displacement and initial angle affect the initial velocity of a projectile?

The initial velocity of a projectile is directly proportional to both the displacement and the initial angle. This means that as the displacement or initial angle increases, the initial velocity will also increase.

3. Can the initial velocity of a projectile be negative?

Yes, the initial velocity of a projectile can be negative if the initial angle is directed downwards. This indicates that the projectile is initially moving in the opposite direction of the positive y-axis.

4. What is the unit of measurement for initial velocity in projectile motion?

The initial velocity in projectile motion is typically measured in meters per second (m/s).

5. Is the initial velocity of a projectile constant throughout its motion?

No, the initial velocity of a projectile is only constant at the moment of release. As the projectile moves, its velocity will change due to the effects of gravity and air resistance.

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