How long in seconds was the kangaroo in the air?

[annyaroo]

I have a problem which is a kangaroo jumps to a vertical height of 227 cm. how long in seconds was the kangaroo in the air? so far i have 2.27m=0+1/2 (9.8)t^2 = 2.27=4.9t^2 ~ 4.9/2.27= 2.15859, and then i took the square root of 2.15859 and got 3.89 m/s. could you please tell me what i did wrong, or if i am using the right equation?

 

[zwtipp05]

The kangaroo must have an initial velocity in order to reach the height.
There are two ways to do this probelm:

You need to set up two equations:
First, the kangaroo's velocity is zero at the top of the jump so you know that the following equation is valid:
$$0=v_i+gt_{.5}$$

Also we know that the following equation should be true:

$$0=v_i(2t_{.5})+\frac{1}{2}g(2t_{.5})^2$$

Since the kangaroo will end at zero when it hits the ground again.
Solving the system of equations will give you t.


Alternatively, half the time of the jump will be going up and half will be going down.
So
$$2.27 m=\frac{1}{2}(t_{.5})^2$$

 

[quicknote]

Hello,

Thank you for sharing your problem with me. First of all, I would like to clarify that the equation you used is correct for finding the time (t) when an object reaches a certain height (h) after being launched with an initial velocity (u) and experiencing a constant acceleration (a). The equation is h = u*t + 1/2*a*t^2.

However, in this case, we do not have the initial velocity (u) of the kangaroo. We only know that it jumped to a vertical height (h) of 227 cm. Therefore, we cannot use this equation to find the time (t) in seconds.

Instead, we can use the equation v^2 = u^2 + 2*a*h, where v is the final velocity of the kangaroo at the highest point of its jump. Since the kangaroo's final velocity at the highest point is zero, we can rewrite the equation as 0 = u^2 + 2*a*h.

Now, we can solve for the initial velocity (u) by substituting the values of acceleration (a = 9.8 m/s^2) and height (h = 2.27 m) into the equation. This gives us u = √(2*a*h) = √(2*9.8*2.27) = √44.936 = 6.7 m/s.

Finally, we can use the equation v = u + a*t to find the time (t) in seconds. Since the final velocity (v) is zero, we can rewrite the equation as 0 = u + a*t and solve for t. This gives us t = -u/a = -6.7/9.8 = -0.68 seconds.

However, since time cannot be negative, we need to take the absolute value of t, which gives us t = 0.68 seconds. Therefore, the kangaroo was in the air for approximately 0.68 seconds.

I hope this helps to clarify your doubts. Keep up the good work with your calculations!

Best regards,