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3 years ago

A stone was dropped off a cliff and hit the ground with a speed of 120 ftys. what is the height of the cliff

1 answer:

5 0

Givens:
Acceleration (a) = 32.17 ft/s² as that is the only force acting on the stone in free fall assuming no air resistance

Initial velocity (V1) = 0 ft/s as that it the starting speed of the stone as all objects about to move from rest must start at 0 velocity at rest = 0 velocity

Final velocity (V2) = 120 ft/s

Displacement aka. the height of the cliff (Δd) = ? ft

The kinematic formula we can use is: V2² = V1² + 2(a)(Δd)
Isolate to solve for Δd and just plug in the numbers!
V2² = V1² + 2(a)(Δd)
(120)² = (0)² + 2(32.17)(Δd)
14400 = 2(32.17)(Δd)
$\frac{1400}{2(32.17)}$ = Δd
223.9 = Δd

Therefore, the height of the cliff is 223.9 ft! Hope this helped! :)

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Question 26 (1 Point)

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4 years ago

The magnitude of vector λa is 5. Find the value of λ, if: a = (−6, 8)

Nata [24]

Given :

$\: \:$

$\color{pink}{\rm \: The \:magnitude \:of \:vector\: λa\: is \: {\bold5\:}}$

$\:$

$\color{green}{\rm \: a = (−6, 8)}$

$\:$

To Find :

$\: \:$

$\orange{ \rm\: value \: of \: \bold{ λ \: }}$

$\: \:$

$\rm \: The \: magnitude \: of \: the \: vector \: a \: is \: ||a|| = \sqrt{(-6)^2+ 8^2)} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm = \sqrt{( 36+64)} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\: \: \:\:= \rm\sqrt{100} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \rm \underline{\boxed{\red{ \: = 10 \: }}} \green✓$

$\: \:$

$\rm \: Therefore, \: λ = \cancel{\frac{5}{10} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline { \: \boxed{ \red{\: \rm = 0.5\:}}}{ \green ✓ }$

Hope helps ~

$\color{purple}\frak{SarcasticSmileeᥫ᭡}$

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