The rock has a height <em>y</em> at time <em>t</em> according to
<em>y</em> = 25 m + (60 m/s) sin(32°) <em>t</em> - 1/2 <em>gt</em> ²
where <em>g</em> = 9.8 m/s² is the magnitude of the acceleration due to gravity.
Solve for <em>t</em> when <em>y</em> = 0. The quickest way to do this is with the quadratic formula.
0 = 25 m + (60 m/s) sin(32°) <em>t</em> - 1/2 <em>gt</em> ²
<em>t</em> = (-(60 m/s) sin(32°) + √[(60 m/s)² sin²(32°) - 4 (25 m) (-1/2 <em>gt</em> ²)]) / 2
(ignoring the negative root because that would make <em>t</em> negative)
or approximately
<em>t</em> ≈ 7.2 s
Answer:
45 s
Explanation:
To find the time it takes to stop, we first find the deceleration, a of the car from
v² = u² + 2as and a = (v² - u²)/2s were v = final velocity of car = 0 mph = 0 m/s, u = initial velocity of car = 30 mph = 30 × 1609.34 ft ÷ 3600 s = 13.41 ft/s and s = distance = 300 ft. Substituting the values into a, we ave
a = (v² - u²)/2s = (0² - 13.41²)/2×300 = -0.3 ft/s²
We then find the time for this deceleration from v = u + at ⇒ t = (v - u)/a
t = (v - u)/a = (0 - 13.41 ft/s)/-0.3 ft/s² = - 13.41 ft/s/-0.3 ft/s² = 44.7 s ≅ 45 s
So it takes 45 seconds to stop.
the color violet has the shortest wavelength!
Answer:
Explanation:
m = Mass of water = 2 kg
c = Specific heat of water =
= Change in temperature =
Change in thermal energy is given by
Cale's change in thermal energy was .