How Do You Calculate Projectile Motion with Forces in Multiple Directions?

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To calculate the projectile motion with forces acting in multiple directions, start by recognizing that the problem involves a projectile launched with an initial velocity of 300 ft/s down the y-axis, affected by additional velocities in the negative z and x directions. The forces acting at 60 ft/s in the negative z direction and 45 ft/s in the negative x direction should be treated as constant velocity adjustments rather than traditional forces. To find the angle of elevation (theta) and angle of correction (Beta), apply kinematic equations while considering these adjustments. Additionally, derive the vector-valued function r(t) for the projectile's path, total distance traveled, maximum height, and time to hit the target. A step-by-step approach is essential to navigate the complexities introduced by the additional velocities.
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Homework Statement



A projectile fired down the y-axis with V0 = 300 ft/s, hits a target 500ft away. Assume constant force is acting on projectile at 60ft/s in negative z direction. Assume second constant force acting on projectile in negative x direction at 45ft/s.

Find angle of elevation (theta) of the launch and angle of correction (Beta) in x direction.

Find vector valued function r(t) representing path of projectile.

Find total distance traveled by projectile.

Find maximum height reached by projectile.

Find time it takes projectile to hit target.

Homework Equations


Kinematic equations.

The Attempt at a Solution



The constant force from negative z and negative x directions are completely throwing me off. Help would be appreciated, taking me through step by step. Thank you.
 
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ch2kb0x said:

Homework Statement



A projectile fired down the y-axis with V0 = 300 ft/s, hits a target 500ft away. Assume constant force is acting on projectile at 60ft/s in negative z direction. Assume second constant force acting on projectile in negative x direction at 45ft/s.

Find angle of elevation (theta) of the launch and angle of correction (Beta) in x direction.

Find vector valued function r(t) representing path of projectile.

Find total distance traveled by projectile.

Find maximum height reached by projectile.

Find time it takes projectile to hit target.

Homework Equations


Kinematic equations.

The Attempt at a Solution



The constant force from negative z and negative x directions are completely throwing me off. Help would be appreciated, taking me through step by step. Thank you.

You will need to modify your treatment of the Z motion with the additional velocity they provide. (And the X velocity affects X displacement.)

Note they call it a force, though it's not in the units of Force. They apparently want you to treat it as a constant velocity adjustment.
 
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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}...
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