Find Acceleration

 

What is the range?

A projectile is launched at an angle of 10 and lands 30 s later at the same height as it was launched.
What is the range?
Input your answer in m in scientific e-notation using 3 significant figures.

Solution

θ = 10°
t = 30s
x = ?

v cos(θ) t = x
gt = 2vsin(θ)

v=gt /(2sin(θ))

gt /(2sin(θ)) cos(θ) t = x

gt

²

 cot(θ) /2 = x

x = gt² cot(θ) /2
θ = 10°
t = 30s

g=9.8 m/s²

WolframAlpha: 
 find x: θ = 10 degrees, t = 30, g=9.8, x = g*t² cot(θ) /2 

https://www.wolframalpha.com/input?i=+find+x%3A+%CE%B8+%3D+10+degrees%2C+t+%3D+30%2C+g%3D9.8%2C+x+%3D+g*t%C2%B2+cot%28%CE%B8%29+%2F2 


Google Search:

9.8 m/s^2*(30s)^2*cot(10deg)/2 in m 

How long will it take a log to float from the dam to the grove?

The beavers noticed that swimming from the dam to the grove along the river takes time t₁, and swimming back along the river from the grove to the dam takes time t₂, and t₁ < t₂.

How long (t=?) will it take a log to float from the dam to the grove?



Solution



t₁ (V_s + V_r)  =  L

t₂ (V_s - V_r)  =  L

t  V_r  =  L


 (V_s + V_r)  =  L/t₁

 (V_s - V_r)  =  L/t₂

(V_s + V_r) - (V_s - V_r)   =   L/t₁ - L/t₂ 

2 V_r    =     L(1/t₁ - 1/t₂)

V_r   =    L(1/t₁ - 1/t₂)/2

t =  L/ V_r  = L /  ( L(1/t₁ - 1/t₂)/2)     =  2t₁ t₂ / (t₂ - t₁)

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2 Key Equations