I have a question about an arbitrary projectile being launched and an arbitrary polynomial describing the height(time) = h(t). The question goes onto ask about the velocity at different points in time.
I feel like I'm missing something because if it's height of time there is no horizontal component so how could one know the velocity of the object?
I feel like maybe it's asking to take the derivative for displacement but I'm worried it might be a trick. The question does not specify the vertical velocity. Furthermore, it's clear the object is moving forward since it starts on the top of a cliff with the y-intercept not at 0, and proceeding down the height of the cliff eventually after peak height as time moves forward.
This is about where I am but unsure how to proceed. Any food for thought?
Thank you.
Unless you have a picture or anything else to indicate horizontal motion, I'd take it that the motion occurs only up-and-down and that the (upward) launch from the cliff is just a way of getting an initial non-zero displacement. And presumably the cliff is perfectly vertical and the projectile motion takes place an infinitesimal distance away from the cliff so the projectile doesn't graze it on the way down.
In this scenario, the velocity is $h'(t)$.