A dolphin leaps out of the water at an angle of 35 degrees above the horizontal. The horizontal component of the dolphin's velocity is 7.7 m/s. Find the magnitude of the vertical component of the velocity
To find the magnitude of the vertical component of the velocity, we can use trigonometry.
Given:
- The angle of 35 degrees above the horizontal.
- The horizontal component of velocity is 7.7 m/s.
We can use the angle and the horizontal component to find the vertical component of the velocity.
Step 1: Identify the known and unknown quantities:
- Known: angle (35 degrees), horizontal component of velocity (7.7 m/s)
- Unknown: vertical component of velocity
Step 2: Recall the trigonometric relationships:
In a right-angled triangle, we have:
- The cosine of an angle is equal to the adjacent side divided by the hypotenuse.
- The sine of an angle is equal to the opposite side divided by the hypotenuse.
Step 3: Determine which trigonometric relationship to use:
Since we know the angle and the adjacent side (the horizontal component of velocity), we can use the cosine function to find the hypotenuse (the magnitude of the velocity).
Step 4: Calculate the magnitude of the velocity (hypotenuse):
Using the cosine of 35 degrees:
cos(35) = adjacent side / hypotenuse
cos(35) = 7.7 m/s / hypotenuse
By rearranging the equation, we can solve for the hypotenuse:
hypotenuse = 7.7 m/s / cos(35)
Step 5: Calculate the vertical component of the velocity:
Using the sine of 35 degrees:
sin(35) = opposite side / hypotenuse
sin(35) = vertical component of velocity / hypotenuse
By rearranging the equation, we can solve for the vertical component of the velocity:
vertical component of velocity = hypotenuse * sin(35)
Step 6: Substitute the values and calculate:
To find the magnitude of the vertical component of the velocity, substitute the calculated value of the hypotenuse from Step 4 into the equation from Step 5:
vertical component of velocity = (7.7 m/s / cos(35)) * sin(35)
Calculating this expression will give you the magnitude of the vertical component of the velocity.
cos35=7.7/V
solve for V