an experimental jetplane just after takeoff climbs with a speed of 500km/hr at an angle of 37 degrees with the horizontal. At what rate is the plane gaining altitude?
SOHCATOA
Sin37= v/500
V=500 • sin37
=300.90 ≈ 301 km/h
An experimental plane just after takeoff climbs with a speed of 300 km/h at an angle of 30 degrees with the horizontal. a) At what rate is the plane gaining altitude? (Hint, the vertical component of velocity is the rate that the plane is gaining altitude). b). What is the horizontal component of velocity for the plane? Round answers to the nearest whole number.
500 x sin37 = 300km/hr
500 x sin37= 300km/hr
Well, I gotta say, that experimental jetplane is really taking off! Now, to calculate the rate at which it's gaining altitude, we'll need to break it down.
First, let's find the vertical component of its velocity. To do that, we'll multiply the speed (500 km/hr) by the sine of the angle (37 degrees). But hey, have you ever thought about what would happen if pilots used math puns? They'd definitely be flying by the seat of their pants!
Anyway, back to the question. So, the vertical component of the velocity is given by V vertical = 500 km/hr * sin(37°). And when we calculate that, we get V vertical = 296.48 km/hr. Talk about reaching new heights!
Now, since we're looking for the rate at which the plane is gaining altitude, we just need to convert that vertical velocity to meters per second. Whoa, slow down there, plane! So, let's convert 296.48 km/hr to meters per second.
There are 1000 meters in a kilometer, and 1 hour is equal to 3600 seconds. So, when we crunch those numbers, we find that 296.48 km/hr is equal to 82.36 m/s.
Therefore, the rate at which the plane is gaining altitude is approximately 82.36 m/s. I guess you can say the plane is really soaring to new heights at a pretty impressive speed!
To determine the rate at which the plane is gaining altitude, we need to analyze the given information about its speed and angle of ascent.
The speed of the plane, given as 500 km/hr, refers to its ground speed or horizontal velocity. This means that the plane is covering a horizontal distance of 500 km in one hour.
Since we are interested in the rate at which the plane is gaining altitude, we need to focus on the vertical component of its velocity. The angle of ascent, given as 37 degrees, provides us with the information necessary to separate the velocity into horizontal and vertical components.
To find the vertical component of the velocity, we can use trigonometry. The vertical component of the velocity can be determined by multiplying the total speed by the sine of the angle of ascent:
Vertical velocity = Speed × sin(Angle)
Vertical velocity = 500 km/hr × sin(37°)
To calculate the answer, input these values in a calculator to get the vertical velocity of the plane.