PHYSICS 111 SI 2D MOTION; PROJECTILE MOTION

You are adding vectors of length of 20 and 40 units. What is the only possible resultant magnitude?  A)18  B) 37  C) 64  D) 100

Answer: 37  If scalar, Max value is 60 units  If scalar, min value is 20  Says the value is a Vector, so have different directions  Has to be between 60 and Is the only option that works

Adding Vectors  Add the following vectors and determine the resultant.  5.0 m/s, 45 deg and 2.0 m/s, 180 deg

Mag: 3.85 At 66.5 degrees from –x axis

 Given that A + B = C, and that lAl 2 + lBl 2 = lCl 2, how are vectors A and B oriented with respect to each other? (1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other

Answer: The are perpendicular  Vectors satisfy the Pythagorean Theorem, with suggest they are a right triangle, where a and b would be perpendicular at a 90 degree angle

 Given that A + B = C, and that lAl + lBl = lCl, how are vectors A and B oriented with respect to each other? (1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45° to each other 5) they can be at any angle to each other

Answer: Parallel but in same direction  The only time vector magnitudes will simply add together is when the direction does not have to be taken into account

 From the same height (and at the same time), one ball is dropped and another ball is fired horizontally. Which one will hit the ground first?  (1) the “dropped” ball  (2) the “fired” ball  (3) they both hit at the same time  (4) it depends on how hard the ball was fired was fired  (5) it depends on the initial height

Answer: The Same Time  In the Y direction, both have the same acceleration  -g  Therefore, they will hit the ground at the same time X movement does matter

Example Problem  You drop your phone as you are walking at a constant velocity of 3 m/s at a height of 1.5 m.  Determine how long it takes your phone to hit the ground and at what velocity

Answer:  Time:  Use equation Delta Y = Vi(t) +.5(a)(t^2)  Delta t = square root of ((2*-1.5)/-9.8) = =.55 seconds  Velocity:  Know that the X direction has no acceleration Know Vi and Vf are the same, 3 m/s  For the Y direction Use Vf= Vi + a(t) Vf= 0 + (-9.80)(.55) = m/s Finally use C^2 = A^2 + B^2 Vf = Square root of [(.5.39^2) + (3^2)]

Practice Problem  You throw a baseball to your friend. You throw at an angle of 24 degrees and with an initial velocity of 30 m/s. Determine the maximum height the ball will reach.

Answer:  Determine Vx and Vy  30 Cos24 = Vx =27.4 m/s  30 Sin 24 = Vy = 12.2 m/s  Use equation Vf ^2 = Vi ^2 + 2 a ( delta y) Delta Y is only for the first half the throw (not looking at the ball going down) Vf= 0 because comes to rest at top before changing directions 0^2 = 30 ^2 + 2(-9.8) ( Y) (0-30) / (2 * -9.8) Y= 1.53 m

Resources:  dimensional-motion/old-projectile-motion/v/projectile- motion-part-1 dimensional-motion/old-projectile-motion/v/projectile- motion-part-1  Link to FREE Khan Academy videos  In-depth videos that go over problems Multiple subject are covered For physics: 1-D and 2-D Motion Force and Newton’s Laws Work, Energy, Momentum,…. Also has trigonometry, chemistry, ect….