Physics, 15.04.2020 16:08 tynitenaire

A rock is thrown upward from a bridge into a river below. The function f(t)=−16t2+44t+88 determines the height of the rock above the surface of the water (in feet) in terms of the number of seconds t since the rock was thrown.

What is the bridge's height above the water?

feet

How many seconds after being thrown does the rock hit the water?

seconds

How many seconds after being thrown does the rock reach its maximum height above the water?

seconds

What is the rock's maximum height above the water?

Answers: 2

Show answers

Answers

Answer from: Diego4519

1) 88 ft

2) 4.09 s

3) 1.38 s

4) 118.2 m

Explanation:

For an object thrown upward and subjected to free fall, the height of the object at any time t is given by the suvat equation:

$h(t) = h_0 + ut - \frac{1}{2}gt^2$ (1)

where

h_0 is the height at time t = 0

is the initial vertical velocity

g=32 ft/s^2 is the acceleration due to gravity

The function that describes the height of the rock above the surface at a time t in this problem is

f(t)=-16t^2+44t+88 (2)

By comparing the terms with same degree of eq(1) and eq(2), we observe that

h_0 = 88 ft

which means that the rock is at height h = 88 ft when t = 0: therefore, this means that the height of the bridge above the water is 88 feet.

The rock will hit the water when its height becomes zero, so when

f(t)=0

which means when

0=-16t^2+44t+88

First of all, we can simplify the equation by dividing each term by 4:

0=-4t^2+11t+22

This is a second-order equation, so we solve it using the usual formula and we find:

$t_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-11\pm \sqrt{(11)^2-4(-4)(22)}}{2(-4)}=\frac{-11\pm \sqrt{121+352}}{-8}=\frac{-11\pm 21.75}{-8}$

Which gives only one positive solution (we neglect the negative solution since it has no physical meaning):

t = 4.09 s

So, the rock hits the water after 4.09 seconds.

Here we want to find how many seconds after being thrown does the rock reach its maximum height above the water.

For an object in free fall motion, the vertical velocity is given by the expression

v=u-gt

where

u is the initial velocity

g is the acceleration due to gravity

t is the time

The object reaches its maximum height when its velocity changes direction, so when the vertical velocity is zero:

v=0

which means

0=u-gt

Here we have

u=+44 ft/s (initial velocity)

g=32 ft/s^2 (acceleration due to gravity)

Solving for t, we find the time at which this occurs:

$t=\frac{u}{g}=\frac{44}{32}=1.38 s$

The maximum height of the rock can be calculated by evaluating f(t) at the time the rock reaches the maximum height, so when

t = 1.38 s

The expression that gives the height of the rock at time t is

f(t)=-16t^2+44t+88

Substituting t = 1.38 s, we find:

f(1.38)=-16(1.38)^2 + 44(1.38)+88=118.2 m

So, the maximum height reached by the rock during its motion is

$h_{max}=118.2 m$

Which means 118.2 m above the water.

Answer from: Quest

what best describes physical development during adolescence is the development of secondary sex characteristics happens at a rate unique to each individual.

Answer from: Quest

Idont understand the question

Another question on Physics

Physics, 21.06.2019 21:20

Which of the following explains why it took so long for the public to accept the negative health effects of smoking? a)people were waiting for counter reasons, and those were presented.b)scientists had not completely finalized their results, which took 30 years.c)cigarettes were cheaply available and media channels were very inefficient.d)cigarette manufacturers were trying hard to bring an alternative into the market

Answers: 3

Answer

Physics, 22.06.2019 19:00

Review multiple-concept example 7 in this chapter as an aid in solving this problem. in a fast-pitch softball game the pitcher is impressive to watch, as she delivers a pitch by rapidly whirling her arm around so that the ball in her hand moves in a circle. in one instance, the radius of the circle is 0.626 m. at one point on this circle, the ball has an angular acceleration of 66.1 rad/s2 and an angular speed of 12.6 rad/s. (a) find the magnitude of the total acceleration (centripetal plus tangential) of the ball. (b) determine the angle of the total acceleration relative to the radial direction.

Answers: 3

Answer

Physics, 22.06.2019 20:00

Aspectroscope breaks light up into its colors, allowing scientists to analyze light from the solar system and universe. by studying the spectral line patterns, widths, strengths and positions, scientists can determine the speed, position, and of celestial bodies. a) age b) origin c) rotation d) temperature

Answers: 1

Answer

Physics, 22.06.2019 21:20

16. a brave but inadequate rugby player is being pushed backward by an opposing player who is exerting a force of 800 n on him. the mass of the losing player plus equipment is 90.0 kg, and he is accelerating at 1.20m/s2 size 12{1 "." "20"" m/s" rsup { size 8{2} } } {} backward. (a) what is the force of friction between the losing player’s feet and the grass? (b) what force does the winning player exert on the ground to move forward if his mass plus equipment is 110 kg? (c) draw a sketch of the situation showing the system of interest used to solve each part. for this situation, draw a free-body diagram and write the net force equation.

Answers: 2

Answer

You know the right answer?

A rock is thrown upward from a bridge into a river below. The function f(t)=−16t2+44t+88 determines...

Questions