A seagull drops a sea urchin onto the rocks below from a height of 80 m . The function \( h(t)=-5 t^{2}+80 \) models the height of the urchin, in metres, and \( t \) is the time in seconds. When will the sea urchin hit the rocks?

To find out when the sea urchin hits the rocks, we need to determine when the height \( h(t) \) is equal to zero. To do this, we set the equation \( -5t^2 + 80 = 0 \). Rearranging gives us \( 5t^2 = 80 \). Dividing both sides by 5 results in \( t^2 = 16 \). Taking the square root of both sides gives \( t = 4 \) seconds. So, the sea urchin will hit the rocks after 4 seconds! Now, here's a fun fact: Seagulls are incredibly resourceful birds! They often drop shellfish onto rocks to crack them open, showcasing not just survival skills but also an impressive understanding of physics—much like the calculation we just did! Additionally, dropping objects in a vacuum versus a real environment reveals fascinating differences! While the urchin hit the rocks due to gravity pulling it down, in a vacuum, it would still fall, but without air resistance. Every drop teaches us something about the forces at play in our world—how cool is that?