Note die expression: y = x^2. Which statement is most consistent with this expre

Question

Note die expression: y = x^2. Which statement is most consistent with this expression? if x doublet, then y quadruples if y doubles, then x quadruples if x triples, then y doubles if x doubles, then y doubles y is greater than x An object is thrown vertically and has an upward velocity of 25 m/s when it reaches one-fourth of its maximum height above its launch point. What is the maximum height of the object? 50 m 76.37 m 32.46 m 42.52 m 11.68 m A ball is shot with a velocity of 36 m/s at an angle of 30 degree from the top of a 20 m tall building. What is the horizontal distance the ball travels when it hits the ground? A cart is given an initial velocity of 5.0 m/s and experiences a constant acceleration of 2.5 m/s^2,. What is the magnitude of the cart's displacement during the first 6.0 s of its motion? At the top of a cliff 100 m high. Raoul throws a rock upward with velocity 20 m/s. How much later should be drop a second rock from rest so both rocks arrive simultaneously at the bottom of the cliff? An airplane starts from rest and accelerates at 12.1 m/s^2. What is its speed at the end of a 500 m runway? The position of a particle moving along the x-axis is given by x = 30t^2 - 30t^4, where x is in meters and t is in seconds What is the position of the panicle when it achieves its maximum speed in the positive x-direction? When a drag strip vehicle reaches a velocity of 60 m/s, it begins a negative acceleration by releasing a drag chute and applying its brakes. While reducing its velocity bock to zero, its acceleration along a straight line path is a constant -9.5 m/s^2,. What displacement does it undergo during this deceleration period? A car slows down from a speed of 31 m/s to a speed of 12 m e over a distance of 380 m. How long does this take, assuming constant acceleration?

Explanation / Answer

1) y = x^2

if x' = 2x

y' = x'^2 = (2x)^2 = 4 x^2 = 4y

y quadruples.

Ans(A)

2) suppose initial velocity of object is v.

then for maximum height,using energy conservation

mv^2 /2 + 0 = 0 +   mgh

h = v^2 /2g

for h/4 .

energy conservation ( PE +KE)

mv^2 /2 + 0 = mg(h/4) + mvf^2 /2

v^2 /2   = g (v^2 / 8g) + (25^2/ 2)

v^2 /2 - v^2/8 = 625/2

v = 28.87 m/s

h = v^2 /2 g = 28.87^2 / 2x9.81 = 42.5 m

Ans(D)

3. time needed to raech ground,

-20 = (36sin30)t - 9.81t^2 /2

4.905t^2 - 18t - 20 = 0

t =4.56 s

horizontal distance = vx *t = 36cos30 x 4.56 = 142 m

Ans(A)

4. d = ut + at^2 /2

d = 5x6   + 2.5 x 6^2 /2

d = 75 m

Ans(D)

5. time taken by rock thrown upward

using , d = ut + at^2 /2

-100 = 20t - 9.81t^2/2

4.905t^2 - 20t - 100 = 0

t = 6.99 s

time taken by rock that is dropped.

-100 = 0 - 9.81t^2 /2

t = 4.51 s

time diff = 6.99 - 4.51 = 2.48 s

ans(D )

please don't post too many questions at a time

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