Tutorial for Projectile Motion Problems. Components of Velocity. If an object is launched at an angle, its velocity is not perfectly horizontal (x direction), nor is it perfectly vertical (y direction).
Vx=V0 cos Θ=30 cos 25= 27.19 m/s
V0y=V0 sin Θ= 30 sin 25=12.68 m/s
V1: 30 m/s
g= -9.8 m/s2
A rocket is launched from the ground and is aimed 2500 m away. If it reaches a maximum height of 200 meters, how fast must it be going when it leaves the ground (find Vy and Vx)? At what angle must it be launched? (Hint: find time first using cliff problems)
X: 2500 m
Y: 200 m
To find the initial velocity (V0), find Vx and V0y. First find time using the initial velocity in the y direction as zero.
Vx= x = 195.62 m/s
= 62.62 m/s
3. A basketball player jumps up at 15 m/s at an angle of 50 degrees. At what time will he be 2 meters away (horizontally) from where he jumped?
Vx=V0 cos Θ=9.64 m/s
T=x= .21 s
V0: 15 m/s
4. A football is kicked with an initial velocity of 55 m/s at an angle of 60 degrees. At what times will it pass 5 meters above the ground? (you can use quadratic formula in the calculator)
V0y= V0 sin Θ= 47.63 m/s
V0: 55 m/s
The ball will pass 2 meters high twice.
You can use the quadratic formula to find the two times
ax2+ bx + c=0
Make equation look like this
5. A baseball is thrown into the air with a velocity of 27.5 m/s at an angle of 45 degrees. What will its velocity be after 3 seconds? (Hint: find its Vy and Vx at 3 seconds, use the Pythagorean Theorem).
V0: 27.5 m/s
T= 15 sec.
Vy= V0 sin Θ=19.45 m/s
Vx= V0 cos Θ= 19.45 m/s
6. A rocket is shot up into the air. If it has a range of 1000 m, and reaches a height of 800 m, what angle was it shot up at and what was its initial velocity?
You must first find the half way time, how long it the rocket to drop the 800 m; set V1y equal to zero for this.
Y= 800 m
Next, find the total time by doubling the half way time
Ttotal= 25.56 seconds
Find Vx using the given distance (x) and the total time
Find V1y by setting V2y equal to zero and using the half way time
Find the V1 by using the Pythagorean Theorem with V1y and Vx.
Find the angle that it is launched at by using the tangent function
7. At what times will a rocket launched at an angle of 37 degrees and a velocity of 400 m/s pass 100 m high? Use Quadratic formula for this.
Find V1y first:
V0= 400 m/s
To find the two times that the rocket passes that height, you must use the Quadratic formula: Set y=V0yt+1/2 gt2 to look like ax2+ bx+c=0. You are solving for t, so your A value is -4.9, your B value is 240.73 m/s (V0y), and your C value is -100 . Use the calculator to plug in and find the two times it passes those two heights.
T1= .42 s
t2= 48.71 s