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Honors Physics – Review for relative velocity, adding vectors, and projectile motion Complete the following problems.

1. Assume that you drop a bag of snacks while riding in an airplane that is flying West at 800 km/hr. Will the bag fall straight down, or will it angle toward the front or back of the airplane? Explain.

Bag will fall straight down because you and the bag of snacks are traveling with the same vertical velocity.

2. You are standing on a high cliff above the ocean. You drop a pebble, and it strikes the water 4 seconds later. Ignoring the effects of air resistance, how fast was the pebble traveling just before striking the water?

y-direction 𝑣! = 0

𝑎! = −9.8𝑚𝑠!

∆𝑡 = 4  𝑠𝑒𝑐𝑜𝑛𝑑𝑠

∆𝑦 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

𝑣!! = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛  (𝑎𝑠𝑘𝑒𝑑  𝑡𝑜  𝑓𝑖𝑛𝑑  𝑡ℎ𝑖𝑠)

𝑣!" =  𝑣!" + 𝑎!Δ𝑡

𝑣!" =  0

𝑚𝑠+ −9.8

𝑚𝑠!   4  seconds =  −𝟒𝟎

𝒎𝒔

3. Give an example of each of the following: a. Vector – something with a magnitude and direction. Ex. velocity, displacement, acceleration

b. Scalar – anything with a magnitude only. Ex. speed, distance. c. Resultant – addition or subtraction of two or more vectors. Ex. an airplane

d. Projectile Motion – an object is launched into the air at an angle and then only the force of gravity

acts on it. The object follows a parabolic path. Football kicked.

e. Horizontal Projectile Motion – an object is launched with an initial velocity that only has a horizontal component. There is no vertical component to the velocity. The object follows half of a parabolic path and only the force of gravity acts on the object.

4. What happens to the acceleration of a ball in free fall if the ball’s mass is cut in half? Acceleration due to gravity is not dependent on mass. The acceleration is the same, -9.8 m/s2.

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5. A rock climber drops a piton from the top of a cliff. If the piton passes you with a speed of 7.00 m/s, how fast will the piton be traveling 2.0 seconds later?

y-direction

𝑣!" = −7.00𝑚𝑠

𝑣!" = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

𝑎! = −9.8𝑚𝑠!

∆𝑡 = 2.0  𝑠

∆𝑦 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

𝑣!" =  𝑣!" + 𝑎!Δ𝑡

𝑣!" =  −7.00𝑚𝑠+ −9.8

𝑚𝑠!   2.0  seconds =  −𝟐𝟕

𝒎𝒔

6. You throw a ball straight up at 30 m/s. How many seconds elapse before it is traveling downward at 10 m/s?

y-direction

𝑣!" = 30𝑚𝑠

𝑣!" = −10  𝑚/𝑠

𝑎! = −9.8𝑚𝑠!

∆𝑡 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

∆𝑦 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

𝑣!" =  𝑣!" + 𝑎!Δ𝑡

Δ𝑡 =𝑣!" − 𝑣!"

𝑎!

Δ𝑡 =−10𝑚𝑠 − 30  𝑚/𝑠

−9.8𝑚𝑠!  = 𝟒  𝒔𝒆𝒄𝒐𝒏𝒅𝒔

7. The world’s highest suspension bridge is the Royal Gorge Bridge in Colorado. The bridge spans the top of

the gorge, which rises 321 m above the Arkansas River. Suppose you kick a little rock horizontally off the bridge. The rock hits the water so that the magnitude of its horizontal displacement is 45.0 m. Find the speed at which the rock was kicked.

x-direction y-direction 𝑣! = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

𝑎! = 0

∆𝑡 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

∆𝑥 = 45.0  𝑚

𝑣! = 0

𝑎! = −9.8𝑚𝑠!

∆𝑡 = 𝑢𝑛𝑘𝑛𝑜𝑤𝑛

∆𝑦 = −321  𝑚

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∆𝑦 =12𝑎!∆𝑡!

Δ𝑡 =  2  Δ𝑦𝑎!

=  2  (−321  𝑚)

−9.8𝑚𝑠!= 8.09383  𝑠𝑒𝑐𝑜𝑛𝑑𝑠

Δ𝑥 = 𝑣!Δ𝑡

𝑣! =  Δ𝑥Δ𝑡

=  45.0  𝑚

8.09383  𝑠𝑒𝑐𝑜𝑛𝑑𝑠= 𝟓.𝟓𝟔

𝒎𝒔

8. A plane travels at a velocity of 455 km/hr South. The wind is blowing from the East at a speed of 35 km/hr. What is the relative velocity? If the flight is 2.5 hours long, where does the plane land with respect to the location where the plane took off?

Add vectors to find relative velocity. x-component is – 35 km/hr (it is blowing to the West from the East) y-component is -455 km/hr (it is traveling South) Relative velocity is the resultant (use the Pythagorean Theorem)

𝑐 =   𝑎! + 𝑏!

𝑐 =   (−35𝑘𝑚ℎ𝑟)! + −455

𝑘𝑚ℎ𝑟

!

= 456𝑘𝑚ℎ𝑟

Angle is determined by using tangent and adding to 180 because it is in the third quadrant

tan!!𝑜𝑝𝑝𝑎𝑑𝑗

=   tan!!455 𝑘𝑚ℎ𝑟35 𝑘𝑚ℎ𝑟

= 86  𝑑𝑒𝑔𝑟𝑒𝑒𝑠

Relative Velocity is 456 km/hr at 266 degrees Without the wind the airplane would land due South of its location. With the wind it will land West of South. The distance South is based on the wind’s velocity and the time.

∆𝑥 =  𝑣!∆𝑡 = 35𝑘𝑚ℎ𝑟

2.5  ℎ𝑜𝑢𝑟𝑠 =  88  𝑘𝑚  𝑊𝑒𝑠𝑡  𝑜𝑓  𝑆𝑜𝑢𝑡ℎ