What Are the Key Equations for Projectile Motion?

[sehar100]

A ball is thrown into the air from ground level. After a time t = 3 s, the ball has traveled to a position x1 = 27 m to the right of and y1 = 9 m up from where it was thrown (at this time, the x and y components of the ball's velocity are still positive). The axes show the x and y directions to be considered positive.

b) What was the y component of the initial velocity of the ball?

v0y = m/s

c) What was the initial speed of the throw?

v0 = m/s
d) What was the initial angle of the throw relative to the horizontal? Please enter your answer in degrees.

q0 = °
e) What is the height of the ball at the top of its path?

h = m


2. An Archer shoots an arrow horizontally at 250 feet per second. The bullseye on the target and the arrow are initially at the same height. If the target is 60 feet from the archer, how far below the bullseye (in feet) will the arrow hit the target? Neglect any effects of air resistance.

d = feet

At t = 0, an object is projected with a speed v0 = 35 m/s at an angle q0 = 20° above the horizontal.The axes on the diagram show the x and y directions that are to be considered positive.

For parts a-g, calculate the requested quantities at t = 7 s into the flight:
a) The vertical acceleration of the object:

ay = m/s2
b) Its horizontal acceleration:

ax = m/s2
c) Its vertical velocity:

vy = m/s
d) Its horizontal velocity:

vx = m/s
e) The angle to the horizontal at which the object is traveling (an angle above the horizontal should be reported as a positive number; an angle below the horizontal should be reported as a negative number). Please give your answer in degrees.

angle = °
f) Its vertical displacement, from where it started:

y = m
g) Its horizontal displacement, from where it started:

x = m
h) At what time does the object reach its maximum height?

tymax = s

3. A small airplane flies at 60 m/s relative to the air. The wind is blowing at 20 m/s to the south. The pilot heads this plane east.

c) What direction must the pilot head his plane in order to travel due east relative to the ground? Give the angle in degrees measured north of east.

angle = °

(d) What will be the speed of the plane,v, relative to the ground with this new heading?

v = m/s

4. A river 700 ft wide flows with a speed of 10 ft/s with respect to the earth. A woman swims with a speed of 5 ft/s with respect to the water. a) If the woman heads directly across the river, how far downstream is she swept when she reaches the opposite bank?

d1 = ft
b) If she wants to be swept a smaller distance downstream, she heads a bit upstream. Suppose she orients her body in the water at an angle of 37° upstream (where 0° means heading straight across, as in part (a)), how far downstream is she swept before reaching the opposite bank?

d2 = ft
c) For the conditions of part (b), how long does it take for her to reach the opposite bank?

t = s

5. a) A vector has a magnitude of A = 20 m and makes an angle of q = 68° with the negative x-axis.

What are the x and y components of this vector?

x-component: m

b) The x component of a vector is 18 m and the y component of a vector is 24 m. What is the magnitude and direction (with respect to the positive x-axis) of this vector?

magnitude: 30
direction: °

 

[Saladsamurai]

These are all projectile motion. What are the equations for projectile motion?
Use should have used the template instead of erasing it. Then you would have seen that we do not do work for you; you must make an attempt before we help.

Casey