Solving for 3 variables in projectile motion problem

AI Thread Summary
The discussion focuses on solving a projectile motion problem involving a dart thrown at a 30-degree angle from a height of 1.6 meters, landing 20 meters away. Key equations for vertical and horizontal motion are provided, including the effects of gravity on the dart's trajectory. Participants express uncertainty about isolating variables and understanding the physical meaning of initial height (y1) and final height (y). It is suggested that the initial speed can be expressed in terms of its horizontal (vx) and vertical (vy) components using trigonometric relationships. The conversation emphasizes the need to apply the equations systematically to find the initial speed, maximum height, and impact speed of the dart.
babacanoosh
Messages
36
Reaction score
0

Homework Statement



A dart is thrown at a 30 degree angle above the horizontal from a height of 1.6 meters. It hits the ground 20 meters away.

a) find the initial speed?
b)what is the maximum height reached by the dart (relation to the ground)?
c)what is the speed of the dart as it hits the ground?






Homework Equations



y= y1 + Vy1t - 9.8t^2
Vy = Vy1^2 - 2(9.8)(y - y1)
Vy= Vy1 - 9.8t

The Attempt at a Solution



x1 = 20
x=0
t=?
a=-9.8
y1=?
y=?


I understand that I most likely need to use the following three equations in order to isolate one variable. I am not sure which variable/how to.
 
Physics news on Phys.org
Do you know what y1 (physically) means? Because its value is given in the problem.
So is that of y.

If you call the initial speed v, then you can rewrite v in terms of vx and vy and the angle (30 degrees).
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Projectile Motion Problem Involving Initial Velocity and Gravity Only
Replies
11
Views
1K
Find the height of a lamp based on the velocities of projectiles
Replies
40
Views
2K
Projectile Motion Experiment: Results Too High?
Replies
2
Views
2K
Is the y-component of projectile motion acceleration equal to gravity?
Replies
8
Views
2K
Projectile Motion with Unknown Initial Height
Replies
7
Views
3K
Projectile Motion: time it takes for projectile to hit truck
Replies
15
Views
3K
Uniform Circular Motion and Projectile Motion Help
Replies
14
Views
2K
Finding two variables in projectile motion
Replies
23
Views
4K
Why does this not work? Projectile Motion problem for Dynamics Class
Replies
19
Views
3K
Need clarification of projectile motion
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top