A squirrel sees a BIG acorn being thrown from a tree by a chipmunk and attempts to snatch it. The acorn is thrown from a 10.0 m high branch and with a horizontal velocity of 1.1 m/s. The squirrel on the ground is 5.0 m from the base of the tree. What is the of the squirrel’s average velocity if it grabs the acorn in its mouth just as it touches the ground?
I need this in by 9 minutes.. can someone help?
it takes about √2 sec for the acorn to reach the ground
the direction the acorn is thrown, relative to the squirrel's position is a big factor
... the question is a little vague
h = 0.5g*t^2 = 10m.
4.9t^2 = 10,
t = 1.43s. = Fall time.
d = V*T = 1.1 * 1.43 = 1.57m from base of tree.
d = V*t = 5-1.57 = 3.43m.
V*1.43 = 3.43,
V = 2.40 m/s.
To find the squirrel's average velocity, we need to determine the time it takes for the acorn to reach the ground. We can use the horizontal velocity given (1.1 m/s) to calculate the time it takes for the acorn to travel the horizontal distance of 5.0 m.
The formula for time is:
time = distance / velocity
In this case, the distance is 5.0 m and the velocity is 1.1 m/s. Plugging these values into the formula, we get:
time = 5.0 m / 1.1 m/s = 4.55 s (rounded to two decimal places)
Now that we know the time it takes for the acorn to reach the ground, we can calculate the vertical distance traveled by the acorn using the formula for vertical motion:
distance = (1/2) * acceleration * time^2
The acceleration due to gravity is approximately 9.8 m/s^2. Plugging in the values, we get:
distance = (1/2) * 9.8 m/s^2 * (4.55 s)^2
distance = 104.85 m (rounded to two decimal places)
The squirrel starts at a height of 10.0 m and the acorn reaches the ground at a height of 0 m. Thus, the vertical distance covered by the squirrel is 10.0 m - 0 m = 10.0 m.
To find the average velocity, we divide the total distance covered (10.0 m) by the time taken (4.55 s):
average velocity = 10.0 m / 4.55 s = 2.20 m/s (rounded to two decimal places)
Therefore, the squirrel's average velocity when it grabs the acorn in its mouth just as it touches the ground is 2.20 m/s.